Light helps us see the world, but simply saying that “light travels in a straight line” is not enough to explain many everyday observations. Why can we see our face in a mirror? Why does a pencil appear bent when partly immersed in water? Why does a rear-view mirror give a wider field of view? Why can a magnifying glass make an object look larger? These questions are explained by reflection and refraction of light.

This chapter is especially important in Class 10 because it combines concepts, ray diagrams, sign conventions, formula-based numericals and applications. The notes below follow the Class 10 NCERT framework and cover the major concepts systematically.

1. Light and Its Basic Behaviour

Light is a form of energy that enables us to see objects. An object is visible when light from it, either emitted by the object or reflected from it, reaches our eyes.

Important sources of light

Objects can be broadly classified as:

• Luminous objects – objects that emit their own light.
  • Sun
  • Electric bulb
  • Candle flame
• Non-luminous objects – objects that do not produce their own visible light but become visible by reflecting light.
  • Book
  • Chair
  • Moon
  • Wall

Rectilinear propagation of light

In a homogeneous transparent medium, light generally travels in a straight line. This property is called rectilinear propagation of light.

It helps explain:

• formation of shadows
• pinhole camera
• eclipses
• straight-line travel of a narrow beam of light

However, when light encounters a different medium or a reflecting surface, its direction may change. Two important phenomena are reflection and refraction.

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2. Reflection of Light

Reflection of light is the phenomenon in which light, after striking a surface, returns into the same medium.

For example, when light falls on a plane mirror, it is reflected back into the surrounding medium.

Examples of reflection

• Seeing your image in a mirror
• Seeing objects in still water
• Reflection from polished metal
• Working of a periscope
• Formation of images by spherical mirrors

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3. Laws of Reflection

Reflection follows two fundamental laws.

First law of reflection

The angle of incidence is equal to the angle of reflection.\[ \angle i = \angle r \]

Here:

• i = angle of incidence
• r = angle of reflection

Second law of reflection

The incident ray, the reflected ray and the normal at the point of incidence all lie in the same plane.

These laws apply to both plane and spherical reflecting surfaces.

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4. Important Terms Related to Reflection

Consider a ray of light striking a reflecting surface.

Incident ray

The ray of light that falls on the reflecting surface is called the incident ray.

Point of incidence

The point where the incident ray strikes the reflecting surface is called the point of incidence.

Normal

A line drawn perpendicular to the reflecting surface at the point of incidence is called the normal.

Reflected ray

The ray that bounces back from the reflecting surface is called the reflected ray.

Angle of incidence

The angle between the incident ray and the normal is called the angle of incidence.

Angle of reflection

The angle between the reflected ray and the normal is called the angle of reflection.

Important: Angles of incidence and reflection are measured from the normal, not from the mirror surface.

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5. Regular and Diffuse Reflection

Reflection can be broadly understood as regular reflection and diffuse reflection.

Regular Reflection	Diffuse Reflection
Occurs on a smooth, polished surface	Occurs on a rough or irregular surface
Reflected rays remain orderly	Reflected rays scatter in different directions
Can produce a clear image	Usually does not produce a clear image
Example: plane mirror	Example: wall, paper

Important misconception

A rough surface does not mean that reflection does not occur.

Reflection still occurs, but because the surface is irregular, the normals at different points have different directions, causing reflected rays to spread out.

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6. Spherical Mirrors

A spherical mirror is a reflecting surface that forms part of a hollow sphere.

There are two main types:

1. Concave mirror
2. Convex mirror

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7. Concave Mirror

A concave mirror has a reflecting surface curved inward, towards the centre of the sphere.

It is also called a converging mirror because parallel rays of light are reflected towards a common point.

Applications of concave mirrors

Concave mirrors are used in:

• shaving mirrors
• makeup mirrors
• dentist’s mirrors
• reflecting telescopes
• headlights and searchlights
• solar furnaces

Why does a concave mirror magnify the face?

When the face is placed between the pole and focus of a concave mirror, the mirror forms a virtual, erect and magnified image.

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8. Convex Mirror

A convex mirror has a reflecting surface curved outward.

It is also called a diverging mirror because reflected rays spread out.

Applications of convex mirrors

Convex mirrors are commonly used as:

• rear-view mirrors in vehicles
• security mirrors in shops
• mirrors at road intersections

Why are convex mirrors used as rear-view mirrors?

A convex mirror:

1. forms an erect image,
2. forms a virtual image, and
3. provides a wide field of view.

Therefore, the driver can see a larger area behind the vehicle.

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9. Important Terms Related to Spherical Mirrors

Pole (P)

The pole is the centre of the reflecting surface of a spherical mirror.

Centre of curvature (C)

The centre of the sphere of which the mirror forms a part is called the centre of curvature.

Radius of curvature (R)

The distance between the pole and centre of curvature is called the radius of curvature.

R = PC

Principal axis

The straight line passing through the pole and centre of curvature is called the principal axis.

Principal focus (F)

When rays parallel to the principal axis strike a concave mirror, they are reflected and meet at a point on the principal axis. This point is called the principal focus.

For a convex mirror, reflected rays appear to come from a point behind the mirror. This point is its principal focus.

Focal length (f)

The distance between the pole and principal focus is called the focal length.

f = PF

For a spherical mirror, the radius of curvature R is related to the focal length f by \[ \boxed{R = 2f} \].

This relationship is important for numerical problems.

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10. Relation Between Radius of Curvature and Focal Length

For a spherical mirror under the standard paraxial approximation: $\boxed{R=2f}$

Therefore:

• If $R=20\text{ cm}$

$f=\frac{20}{2}=10\text{ cm}$

• If $f=15\text{cm}$

$R=2(15)=30\text{ cm}$

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11. Ray Diagrams for Spherical Mirrors

Ray diagrams are extremely important for understanding image formation.

Three standard rays are particularly useful.

Ray 1: Parallel ray

A ray parallel to the principal axis:

• after reflection from a concave mirror, passes through the focus;
• in a convex mirror, appears to come from the focus behind the mirror.

Ray 2: Ray through focus

A ray passing through the focus of a concave mirror is reflected parallel to the principal axis.

Ray 3: Ray through centre of curvature

A ray directed towards the centre of curvature strikes the mirror normally and is reflected back along the same path.

Ray 4: Ray striking the pole

A ray striking the pole follows the laws of reflection, with the principal axis acting as the normal at the pole.

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12. Image Formation by a Concave Mirror

Six Important Positions of an Object

For a concave mirror, we study image formation for six important object positions:

1. Object at infinity
2. Object beyond C
3. Object at C
4. Object between C and F
5. Object at F
6. Object between F and P

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1. Object at Infinity

When an object is extremely far away from the mirror, the rays reaching the concave mirror can be considered to be parallel to the principal axis.

After reflection, these rays converge at the principal focus F.

Image formed

• Position: At F
• Nature: Real and inverted
• Size: Highly diminished or point-sized

Result

Object at infinity → Image at F

Real, inverted and highly diminished

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2. Object Beyond C

When the object is placed beyond the centre of curvature C, one ray parallel to the principal axis and another suitable ray are used to locate the image.

The reflected rays meet between C and F.

Image formed

• Position: Between C and F
• Nature: Real and inverted
• Size: Diminished

Result

Object beyond C → Image between C and F

Real, inverted and diminished

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3. Object at C

When the object is placed exactly at the centre of curvature C, the reflected rays meet at C.

Image formed

• Position: At C
• Nature: Real and inverted
• Size: Same as the object

Result

Object at C → Image at C

Real, inverted and same size

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4. Object Between C and F

When the object is placed between the centre of curvature C and the principal focus F, the reflected rays meet beyond C.

The image is larger than the object.

Image formed

• Position: Beyond C
• Nature: Real and inverted
• Size: Enlarged

Result

Object between C and F → Image beyond C

Real, inverted and enlarged

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5. Object at F

When the object is placed at the principal focus F, the reflected rays become parallel to the principal axis.

Since parallel rays do not meet at a finite distance, the image is considered to be formed at infinity.

Image formed

• Position: At infinity
• Nature: Real and inverted
• Size: Highly enlarged

Result

Object at F → Image at infinity

Real, inverted and highly enlarged

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6. Object Between F and P

When the object is placed between the principal focus F and the pole P, the reflected rays diverge.

When these reflected rays are produced backwards, they appear to meet behind the mirror.

Image formed

• Position: Behind the mirror
• Nature: Virtual and erect
• Size: Enlarged

Result

Object between F and P → Image behind the mirror

Virtual, erect and enlarged

The image formed by a concave mirror depends strongly on the position of the object.

Object Position	Image Position	Nature of Image	Size
At infinity	At F	Real, inverted	Highly diminished
Beyond C	Between C and F	Real, inverted	Diminished
At C	At C	Real, inverted	Same size
Between C and F	Beyond C	Real, inverted	Enlarged
At F	At infinity	Real, inverted	Highly enlarged
Between F and P	Behind mirror	Virtual, erect	Enlarged

Important pattern

For a concave mirror:

Object beyond C → image moves between C and F

Object between C and F → image moves beyond C

Object at F → image at infinity

Object between F and P → virtual, erect and enlarged image

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13. Image Formation by a Convex Mirror

For a convex mirror, the image is always:

• virtual
• erect
• diminished
• formed behind the mirror between P and F

As the object moves farther away, the image approaches the focus.

For an object at infinity, the image is formed approximately at the focus and is highly diminished.

When the object is between infinity and pole of a convex mirror, a diminished, virtual and erect image is formed between pole and focus, i.e. behind the mirror. The image formed is diminished, virtual and erect.

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14. Real and Virtual Images

Understanding this difference is essential.

Real Image	Virtual Image
Formed by actual intersection of light rays	Formed by apparent intersection of light rays
Can generally be obtained on a screen	Cannot be obtained on a screen
Usually inverted	Usually erect
Concave mirror can form real images	Plane mirror and convex mirror form virtual images

Important point

A concave mirror can form either a real or a virtual image, depending on the object’s position.

A convex mirror always forms a virtual, erect and diminished image for a real object.

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15. Sign Convention for Spherical Mirrors

Numerical problems involving mirrors require the Cartesian sign convention.

According to this convention:

• All distances are measured from the pole.
• Distances measured in the direction of incident light are taken as negative.
• Distances measured opposite to the direction of incident light are positive.
• Heights measured upward from the principal axis are positive.
• Heights measured downward from the principal axis are negative.

For the usual arrangement where light travels from left to right:

• Object distance u is generally negative.
• Concave mirror focal length f is negative.
• Convex mirror focal length f is positive.

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16. Mirror Formula

The relationship between object distance, image distance and focal length is: $\boxed{\frac{1}{f}=\frac{1}{v}+\frac{1}{u}}$

where:

• f = focal length
• v = image distance
• u = object distance

Example

Suppose:$\boxed{f=-10\text{ cm}}$

and$\boxed{u=-20\text{ cm}}$

Using: $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

we get: $\frac{1}{10}=\frac{1}{v}-\frac{1}{20}$

Therefore: $\frac{1}{v}=-\frac{1}{20}$

So: $\boxed{v=-20\text{ cm}}$

The negative image distance indicates that the image is formed in front of the mirror.

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17. Magnification Produced by a Mirror

Magnification tells us how large or small the image is compared with the object.

For spherical mirrors: $\boxed{m=\frac{h_i}{h_o}=-\frac{v}{u}}$

where:

• m = magnification
• h_i = height of image
• h_o = height of object
• v = image distance
• u = object distance

Interpretation

• m>1: image is enlarged
• m<1: image is diminished
• m=1: image has the same size
• Positive m : image is erect
• Negative m: image is inverted

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18. Refraction of Light

When light travels obliquely from one transparent medium to another, its direction changes. This phenomenon is called refraction of light.

For example:

• air → glass
• air → water
• water → glass

The apparent bending of a pencil partly immersed in water is an everyday example of refraction. NCERT uses such observations to introduce the idea that what appears visually obvious may be explained differently once the path of light is understood.

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19. Why Does Refraction Occur?

Refraction occurs because the speed of light changes when it enters a different optical medium.

The frequency of light does not change when light passes from one transparent medium to another, but its:

• speed changes
• wavelength changes
• direction may change

Important relationship

$\boxed {v=f\lambda}$

where:

• v = speed of light
• f = frequency
• $\lambda$ = wavelength

When light enters another medium, its frequency remains constant, so a change in speed results in a change in wavelength.

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20. Optical Density

Optical density describes how strongly a medium affects the propagation of light.

A medium with a higher refractive index is optically denser relative to a medium with a lower refractive index.

Examples:

• Air is optically rarer than glass.
• Glass is optically denser than air.

Important clarification

Optical density is not the same as mass density.

A material can have greater mass density without necessarily being optically denser in the sense used in refraction.

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21. Refraction from Rarer to Denser Medium

When light travels from an optically rarer medium to an optically denser medium, it bends towards the normal.

Example:

Air → Glass

The refracted ray bends towards the normal.

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22. Refraction from Denser to Rarer Medium

When light travels from an optically denser medium to an optically rarer medium, it bends away from the normal.

Example:

Glass → Air

The refracted ray bends away from the normal.

Easy memory rule

Rarer → Denser = Towards normal

Denser → Rarer = Away from normal

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23. Laws of Refraction

Refraction follows two important laws.

First law

The incident ray, refracted ray and normal at the point of incidence all lie in the same plane.

Second law — Snell’s Law

For two given media:\[ \boxed{\frac{\sin i}{\sin r}=\text{constant}} \]

This constant is related to the refractive indices of the two media.

More generally : $\boxed{n_1\sin i=n_2\sin r}$

where:

• n₁ = refractive index of the first medium
• n₂ = refractive index of the second medium
• i = angle of incidence
• r = angle of refraction

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24. Refractive Index

The refractive index of a medium tells us how much the speed of light is reduced in that medium compared with vacuum.

It is given by: $\boxed{n=\frac{c}{v}}$

where:

• n = refractive index
• c = speed of light in vacuum
• v = speed of light in the medium

Refractive index has no unit because it is a ratio of two speeds.

Important point

A higher refractive index generally means light travels more slowly in that medium.

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25. Refraction Through a Rectangular Glass Slab

When a ray of light passes through a rectangular glass slab:

1. The ray enters the glass from air.
2. It bends towards the normal.
3. It travels through the glass.
4. It reaches the second surface.
5. It bends away from the normal while emerging into air.

The emergent ray is parallel to the incident ray, although it is shifted sideways.

This sideways shift is called lateral displacement.

Important point

For a rectangular glass slab:

Incident ray ∥ Emergent ray

but the emergent ray is laterally displaced from the original path.

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26. Why Does a Pencil Appear Bent in Water?

Suppose a pencil is partly immersed in water.

Light coming from the underwater portion travels from water to air. During this process, light is refracted.

The eye assumes that light has travelled along a straight path and therefore traces the refracted rays backward.

As a result, the underwater portion appears to be at a different position.

Hence:

The pencil appears bent or displaced at the water surface.

The pencil itself has not actually bent.

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27. Refraction Through a Glass Slab vs Refraction at a Single Surface

Glass Slab	Single Refracting Surface
Light refracts at entry and exit surfaces	Refraction occurs at the interface
Emergent ray can be parallel to incident ray	Direction depends on the two media and geometry
Lateral displacement occurs	Lateral displacement is not necessarily the characteristic result
Two refractions occur	One main interface is considered

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28. Spherical Lenses

A lens is a transparent refracting medium bounded by two surfaces, at least one of which is usually curved.

There are two principal types:

1. Convex lens
2. Concave lens

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29. Convex Lens

A convex lens is thicker at the centre and thinner at the edges.

It generally causes parallel rays of light to converge.

Therefore, it is called a converging lens.

Uses

Convex lenses are used in:

• magnifying glasses
• cameras
• microscopes
• telescopes
• spectacles for correcting hypermetropia
• projectors

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30. Concave Lens

A concave lens is thinner at the centre and thicker at the edges.

It causes parallel rays to diverge.

Therefore, it is called a diverging lens.

Uses

Concave lenses are used in:

• spectacles for correcting myopia
• optical instruments in suitable combinations

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31. Important Terms Related to Lenses

Optical centre (O)

The central point of a lens through which a ray of light passes approximately without deviation for a thin lens is called the optical centre.

Principal axis

The straight line passing through the optical centre and the centres of curvature of the lens surfaces is called the principal axis.

Principal focus

The point on the principal axis where rays parallel to the principal axis converge, or from which they appear to diverge, is called the principal focus.

A lens has two principal foci, one on each side.

Focal length

The distance between the optical centre and principal focus is called the focal length.

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32. Ray Rules for a Convex Lens

Three standard rays are especially useful.

Rule 1

A ray parallel to the principal axis passes through the principal focus after refraction.

Rule 2

A ray passing through the principal focus before reaching the lens emerges parallel to the principal axis.

Rule 3

A ray passing through the optical centre of a thin lens travels approximately undeviated.

These three rules are sufficient to construct most Class 10 lens ray diagrams.

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33. Image Formation by a Convex Lens

1. Object at Infinity

When an object is placed at infinity, the parallel rays of light incident on the concave mirror converge at the principal focus (F). A real, inverted and highly diminished, point-sized image is formed at the focus.

2. Object Beyond the Centre of Curvature

When an object is placed beyond the centre of curvature (C), the reflected rays meet between the centre of curvature (C) and the principal focus (F). A real, inverted and diminished image is formed.

3. Object at the Centre of Curvature

When an object is placed at the centre of curvature (C), the reflected rays meet at the centre of curvature itself. A real, inverted image of the same size as the object is formed at C.

4. Object Between C and F

When an object is placed between the centre of curvature (C) and the principal focus (F), the reflected rays meet beyond the centre of curvature (C). A real, inverted and enlarged image is formed.

5. Object at the Focus

When an object is placed at the principal focus (F), the reflected rays emerge parallel to the principal axis. Therefore, the image is formed at infinity. The image is real, inverted and highly enlarged.

6. Object Between F and P

When an object is placed between the principal focus (F) and the pole (P), the reflected rays diverge and appear to meet behind the mirror when extended backwards. A virtual, erect and enlarged image is formed behind the mirror.

The position of the object determines the position and nature of the image.

Object Position	Image Position	Nature	Size
At infinity	At F	Real, inverted	Highly diminished
Beyond 2F₁	Between F₂ and 2F₂	Real, inverted	Diminished
At 2F₁	At 2F₂	Real, inverted	Same size
Between F₁ and 2F₁	Beyond 2F₂	Real, inverted	Enlarged
At F₁	At infinity	Real, inverted	Highly enlarged
Between F₁ and O	Same side as object	Virtual, erect	Enlarged

Most important case

When an object is placed between the optical centre and focus of a convex lens, the lens produces a:

virtual + erect + magnified image

This is the principle behind a simple magnifying glass.

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34. Image Formation by a Concave Lens

For a real object, a concave lens always forms an image that is:

• virtual
• erect
• diminished
• formed between the optical centre and focus on the same side as the object

This is a highly important comparison with a convex lens.

1. Object at Infinity

When an object is placed at infinity, the rays of light reaching a concave lens are approximately parallel to the principal axis. After refraction, the rays diverge and appear to come from the principal focus (F).

A virtual, erect and highly diminished, point-sized image is formed at the focus.

2. Object at a Finite Distance

When an object is placed at a finite distance from a concave lens, the refracted rays diverge and appear to meet at a point between the optical centre (O) and the principal focus (F) on the same side of the lens as the object.

A virtual, erect and diminished image is formed between the optical centre and the focus. The image is smaller than the object.

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35. Lens Formula

For a thin lens, using the Cartesian sign convention:\[ \boxed{\frac{1}{f}=\frac{1}{v}-\frac{1}{u}} \]

where:

• f = focal length
• v = image distance
• u = object distance

Important distinction

Do not confuse the mirror formula with the lens formula.

Mirror: $\boxed{\frac{1}{f}=\frac{1}{v}+\frac{1}{u}}$

Lens: $\boxed{\frac{1}{f}=\frac{1}{v}-\frac{1}{u}}$

This difference is frequently responsible for errors in numerical problems.

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36. Magnification Produced by a Lens

For a lens: $\boxed{m=\frac{h_i}{h_o}=\frac{v}{u}}$

where:

• m = magnification
• h_i = image height
• h_o = object height
• v = image distance
• u = object distance

Interpretation

• m>1: enlarged image
• m<1: diminished image
• m=1: same size
• Positive m: erect image
• Negative m: inverted image

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37. Power of a Lens

The power of a lens measures its ability to converge or diverge light.

It is given by: $\boxed{P=\frac{1}{f} }$

where f must be expressed in metres.

The SI unit of power is dioptre (D).

Example

If: $f=0.5\text{ m}$

then: $P=\frac{1}{0.5}=+2D$

Therefore, the lens has a power of: $\boxed{+2D}$

Sign of power

• Convex lens → positive power
• Concave lens → negative power

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38. Important Conversion for Power Numericals

If focal length is given in centimetres, convert it into metres first.

For example: $f=20\text{ cm}=0.20\text{ m}$

Therefore: $P=\frac{1}{0.20}=+5D$

Quick formula

If focal length is given in centimetres: $\boxed{P=\frac{100}{f(\text{cm})}}$

with the appropriate sign.

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39. Combination of Thin Lenses

When thin lenses are placed close together, their powers can be added:\[ \boxed{P=P_1+P_2+P_3+\cdots} \]

For example: $P_1=+2D$

and $P_2=-1D$

Then: $P=+2+(-1)=+1D$

The combination therefore has a net converging power of +1D.

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40. Convex Lens vs Concave Lens

Convex Lens	Concave Lens
Works mainly by reflection	Works mainly by refraction
Does not require light to pass through it	Light generally passes through it
Has pole and centre of curvature	Has optical centre and principal foci
Mirror formula: 1/f = 1/v + 1/u	Lens formula: 1/f = 1/v − 1/u
Magnification: −v/u	Magnification: v/u

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41. Concave Mirror vs Convex Mirror

Concave Mirror	Convex Mirror
Reflecting surface curves inward	Reflecting surface curves outward
Converging mirror	Diverging mirror
Can form real or virtual images	Forms virtual images for real objects
Can produce magnified images	Produces diminished images
Used by dentists and in headlights	Used as rear-view mirrors
Field of view is comparatively smaller	Field of view is wider

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42. Reflection vs Refraction

Reflection	Refraction
Light returns into the same medium	Light passes from one medium to another and changes direction
Occurs at a reflecting surface/interface	Occurs when light crosses an interface between transparent media
Follows laws of reflection	Follows laws of refraction
i = r	n₁ sin i = n₂ sin r
Example: mirror	Example: air-glass interface

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43. Mirror vs Lens

Mirror	Lens
Works mainly by reflection	Works mainly by refraction
Does not require light to pass through it	Light generally passes through it
Has pole and centre of curvature	Has optical centre and principal foci
Mirror formula: 1/f = 1/v + 1/u	Lens formula: 1/f = 1/v − 1/u
Magnification: −v/u	Magnification: v/u

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44. Common Misconceptions

Misconception 1: Reflection occurs only in mirrors.

Incorrect.

All surfaces can reflect some light. Smooth surfaces can produce regular reflection and clear images, while rough surfaces produce diffuse reflection.

Misconception 2: A convex mirror can produce an enlarged real image.

For a real object, a convex mirror forms a virtual, erect and diminished image.

Misconception 3: A convex lens always forms a real image.

Incorrect.

If the object is placed between the optical centre and focus, a convex lens forms a virtual, erect and magnified image.

Misconception 4: Refraction changes the frequency of light.

Incorrect.

When light passes from one transparent medium to another, its frequency remains unchanged, while its speed and wavelength may change.

Misconception 5: Angles of reflection and refraction are measured from the surface.

They are measured from the normal.

Misconception 6: Optical density and mass density are identical.

They are different concepts. Optical density is related to how a medium affects the propagation of light.

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45. Important Examination Points

Remember these relationships carefully:

Mirrors

$\boxed{R=2f}$

$\boxed{\frac{1}{f}=\frac{1}{v}+\frac{1}{u}}$

$\boxed{m=-\frac{v}{u}=\frac{h_i}{h_o}}$

Refraction

$\boxed{n=\frac{c}{v}}$

$\boxed{n_1\sin i=n_2\sin r}$

Lenses

$\boxed{\frac{1}{f}=\frac{1}{v}-\frac{1}{u}}$

$\boxed{m=\frac{v}{u}=\frac{h_i}{h_o}}$

$\boxed{P=\frac{1}{f(\text{metre})}}$

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46. How to Solve Numerical Problems Systematically

Use the following method.

Step 1: Write the given quantities

For example: $u=-20\text{ cm}$

$f=-10\text{ cm}$

Step 2: Identify whether it is a mirror or lens

Do not use the mirror formula for a lens or vice versa.

Step 3: Apply the correct sign convention

Do not ignore positive and negative signs.

Step 4: Write the correct formula

For mirror: $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

For lens: $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

Step 5: Substitute values carefully

Keep units consistent.

Step 6: Interpret the answer

Do not stop after calculating v.

Use the sign of v, m, etc., to determine whether the image is:

• real or virtual
• erect or inverted
• enlarged or diminished

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47. Worked Example: Mirror

An object is placed at 20 cm in front of a concave mirror having focal length 10 cm. Find the image distance.

Given: $u=-20\text{ cm}$ $f=-10\text{ cm}$

Using: $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$ $\frac{1}{10}=\frac{1}{v}-\frac{1}{20}$

Therefore: $\frac{1}{v}=-\frac{1}{20}$

Hence: $\boxed{v=-20\text{ cm}}$

The image is formed 20 cm in front of the mirror.

The object is at C, so the image is:

real, inverted and of the same size.

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48. Worked Example: Lens Power

Find the power of a convex lens of focal length 25 cm.

Convert focal length: $25\text{ cm}=0.25\text{ m}$

Use: $P=\frac{1}{f}$ $P=\frac{1}{0.25}$ $\boxed{P=+4D}$

The positive sign indicates a convex lens.

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49. Worked Example: Refraction

Suppose light travels from a medium with refractive index n₁=1.5 to a medium with refractive index n₂=1.0, and the angle of incidence is $30^\circ$.

Using: $n_1\sin i=n_2\sin r$ $1.5\sin30^\circ=1.0\sin r$

Since: $\sin30^\circ=0.5$

we get: $\sin r=0.75$

Thus: $r=\sin^{-1}(0.75)$

approximately: $\boxed{r\approx48.6^\circ}$

The refracted ray bends away from the normal because it is moving from the optically denser medium to the optically rarer medium.

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50. Ray Diagram Strategy

For examination ray diagrams:

1. Draw the principal axis clearly.
2. Mark the relevant points such as P, F and C for mirrors.
3. For lenses, mark O, F and 2F.
4. Draw at least two standard rays.
5. Mark the point where the rays meet or appear to meet.
6. Draw the image with the correct orientation.
7. Label whether the image is real/virtual, erect/inverted and enlarged/diminished.

A correct ray diagram is not just a picture. It should communicate the complete image-formation process.

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51. Real-Life Applications of Reflection and Refraction

Reflection

Rear-view mirrors: Convex mirrors provide a wider field of view.

Shaving mirrors: A concave mirror can produce a magnified erect image when the face is within its focal length.

Headlights: A suitable concave reflecting arrangement can direct light into a useful beam.

Solar furnace: Concave mirrors can concentrate sunlight.

Refraction

Spectacles: Lenses are used to correct refractive errors of vision.

Magnifying glass: A convex lens can produce an enlarged virtual image.

Cameras: Lens systems form images on sensors or film.

Microscopes: Multiple lenses provide magnification.

Telescopes: Lens or mirror systems help form and magnify images of distant objects.

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52. Important One-Line Facts

• Reflection is the process in which light is returned to the same medium after striking a surface.
• Refraction is the change in direction of light when it passes obliquely from one transparent medium to another.
• For reflection at a plane surface, the angle of incidence (i) equals the angle of reflection (r).
• A concave mirror is a converging (focusing) mirror.
• A convex mirror is a diverging mirror.
• A convex lens is a converging lens.
• A concave lens is a diverging lens.
• A convex mirror always forms a virtual, erect, and diminished image for a real object.
• A concave lens always forms a virtual, erect, and diminished image for a real object.
• A convex lens can form either a real or virtual image, depending on the position of the object.
• A concave mirror can form either a real or virtual image, depending on the position of the object.
• For spherical mirrors, R = 2f, where R is the radius of curvature and f is the focal length.
• Mirror formula: 1/f = 1/v + 1/u.
• Lens formula: 1/f = 1/v − 1/u.
• Mirror magnification: m = −v/u.
• Lens magnification: m = v/u.
• Power of a lens: P = 1/f, where f is in metres (m) and P is in dioptres (D).
• SI unit of lens power: dioptre (D).
• A convex lens has positive power (P > 0).
• A concave lens has negative power (P < 0).
• During refraction, the frequency of light remains unchanged; only wavelength and speed change in the new medium.

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Quick Revision Notes

1. Reflection = the phenomenon in which a ray of light is returned into the same medium from a surface.
2. Refraction = the change in direction of propagation of light when it passes obliquely from one transparent medium into another of different optical density.
3. Laws of reflection:
   • i = r
   • The incident ray, the reflected ray, and the normal to the reflecting surface at the point of incidence all lie in the same plane.
4. Concave mirror → converging mirror.
5. Convex mirror → diverging mirror.
6. Relation between radius of curvature and focal length (mirror): R = 2f
7. Mirror formula: 1/f = 1/v + 1/u
8. Linear magnification (mirror): m = −v/u
9. Convex mirror → always forms a virtual, erect, and diminished image (for real objects).
10. Concave mirror → can form a real or a virtual image, depending on the position of the object.
11. Convex lens → converging lens.
12. Concave lens → diverging lens.
13. Lens formula: 1/f = 1/v − 1/u
14. Linear magnification (lens): m = v/u
15. Refractive index (absolute): n = c/v
16. Snell’s law: n₁ sin i = n₂ sin r
17. Rarer medium → denser medium → ray bends towards the normal.
18. Denser medium → rarer medium → ray bends away from the normal.
19. Power of a lens: P = 1/f
20. Power is measured in dioptre (D), where 1 D = 1 m⁻¹.
21. A convex lens has positive power.
22. A concave lens has negative power.
23. The frequency of light remains unchanged during refraction.
24. A rectangular glass slab produces a lateral displacement of the emergent ray, while the emergent ray remains parallel to the incident ray.
25. In numerical problems, always use the Cartesian sign convention consistently.

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Practice MCQs

1. Which phenomenon occurs when light bounces back from a polished surface?

A. Refraction
B. Reflection
C. Dispersion
D. Absorption

Correct Answer: B. Reflection

Explanation: Reflection is the return of light into the same medium after striking a reflecting surface.

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2. The angle of reflection is measured between the reflected ray and the:

A. Mirror surface
B. Incident ray
C. Normal
D. Principal axis

Correct Answer: C. Normal

Explanation: Both the angle of incidence and angle of reflection are measured from the normal to the surface.

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3. Which mirror is commonly used as a rear-view mirror in vehicles?

A. Plane mirror
B. Concave mirror
C. Convex mirror
D. Parabolic mirror

Correct Answer: C. Convex mirror

Explanation: A convex mirror provides a wider field of view and forms a virtual, erect and diminished image.

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4. A concave mirror is called a converging mirror because it:

A. Makes reflected parallel rays diverge
B. Brings reflected parallel rays towards a common point
C. Always forms virtual images
D. Always produces diminished images

Correct Answer: B. Brings reflected parallel rays towards a common point

Explanation: Parallel rays incident on a concave mirror are reflected towards its principal focus.

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5. If the radius of curvature of a spherical mirror is 40 cm, its focal length is:

A. 10 cm
B. 20 cm
C. 40 cm
D. 80 cm

Correct Answer: B. 20 cm

Explanation: R = 2f, so f = R/2 = 40/2 = 20 cm.

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6. Which statement about a convex mirror is correct for a real object?

A. It always forms a real inverted image
B. It always forms a virtual erect diminished image
C. It forms a virtual enlarged image in every case
D. It forms an inverted image in every case

Correct Answer: B. It always forms a virtual erect diminished image

Explanation: A convex mirror forms a virtual, erect and diminished image for a real object.

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7. Which phenomenon explains why a pencil partly immersed in water appears bent?

A. Reflection
B. Dispersion
C. Refraction
D. Diffraction

Correct Answer: C. Refraction

Explanation: Light from the underwater portion changes direction when it travels from water to air, causing the apparent displacement.

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8. When light travels from air into glass obliquely, it generally bends:

A. Away from the normal
B. Towards the normal
C. Along the surface
D. Without changing direction

Correct Answer: B. Towards the normal

Explanation: Glass is optically denser than air, so light bends towards the normal when entering glass obliquely.

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9. Which quantity remains unchanged when light passes from one transparent medium to another?

A. Speed
B. Wavelength
C. Frequency
D. Direction

Correct Answer: C. Frequency

Explanation: During refraction, the frequency of light remains unchanged, while speed and wavelength generally change.

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10. The refractive index of a medium is given by:

A. n=v/c
B. n=c/v
C. n=cv
D. n=c+v

Correct Answer: B. n=c/v

Explanation: Refractive index is the ratio of the speed of light in vacuum to its speed in the medium.

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11. A convex lens is also known as a:

A. Diverging lens
B. Plane lens
C. Converging lens
D. Reflecting lens

Correct Answer: C. Converging lens

Explanation: A convex lens generally brings parallel rays towards its principal focus.

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12. Which type of lens has negative power?

A. Convex lens
B. Concave lens
C. Cylindrical convex lens only
D. Plane glass plate

Correct Answer: B. Concave lens

Explanation: A concave lens has negative focal length under the Cartesian sign convention, giving it negative power.

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13. The SI-related practical unit used for the power of a lens is:

A. Metre
B. Joule
C. Dioptre
D. Newton

Correct Answer: C. Dioptre

Explanation: Lens power is measured in dioptres (D).

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14. The power of a convex lens having focal length \(0.5\) m is:

A. +0.5 D
B. +1 D
C. +2 D
D. −2 D

Correct Answer: C. +2 D

Explanation: P = 1/f = 1/0.5 = +2 D

The positive sign indicates a convex lens.

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15. A convex lens forms a virtual, erect and magnified image when the object is placed:

A. Beyond 2F
B. At 2F
C. Between F and the optical centre
D. At infinity

Correct Answer: C. Between F and the optical centre

Explanation: In this position, the refracted rays diverge and their backward extensions meet to form a virtual, erect and enlarged image.

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16. The formula for magnification produced by a spherical mirror is:

A. m=v/u
B. m=-v/u
C. m=u/v
D. m=-u/v

Correct Answer: B. m=-v/u

Explanation: For a spherical mirror, magnification is m = hᵢ/hₒ = −v/u.

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17. A rectangular glass slab produces lateral displacement because light:

A. Is completely absorbed by the slab
B. Undergoes refraction at its surfaces
C. Stops at the first surface
D. Changes its frequency at every surface

Correct Answer: B. Undergoes refraction at its surfaces

Explanation: Light refracts at both surfaces of the slab. The emergent ray is parallel to the incident ray but shifted sideways.

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18. Which image cannot generally be obtained on a screen?

A. Real image
B. Inverted image
C. Virtual image
D. Image formed by a concave mirror beyond C

Correct Answer: C. Virtual image

Explanation: A virtual image is formed by apparent intersection of rays and cannot be obtained directly on a screen.

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19. If a ray passes through the optical centre of a thin lens, it approximately:

A. Returns along the same path
B. Passes undeviated
C. Always becomes parallel to the principal axis
D. Is completely absorbed

Correct Answer: B. Passes undeviated

Explanation: A ray passing through the optical centre of a thin lens is approximately undeviated.

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20. Which pair is correctly matched?

A. Concave lens — converging lens
B. Convex mirror — converging mirror
C. Convex lens — diverging lens
D. Concave mirror — converging mirror

Correct Answer: D. Concave mirror — converging mirror

Explanation: A concave mirror converges reflected parallel rays, while a convex mirror diverges them. Similarly, a convex lens converges light and a concave lens diverges it.

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Frequently Asked Questions (FAQs)

1. What is the difference between reflection and refraction?

Reflection occurs when light returns into the same medium after striking a surface. Refraction occurs when light enters another transparent medium and its direction changes because its speed changes.

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2. Why is a convex mirror used as a rear-view mirror?

A convex mirror provides a wider field of view and forms a virtual, erect and diminished image. This allows the driver to observe a larger area behind the vehicle.

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3. Can a concave mirror form a virtual image?

Yes. If the object is placed between the pole and focus, a concave mirror forms a virtual, erect and magnified image.

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4. Can a convex lens form a virtual image?

Yes. When the object is placed between the optical centre and principal focus, a convex lens forms a virtual, erect and magnified image.

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5. Why does a coin at the bottom of water appear raised?

Light from the coin undergoes refraction as it travels from water to air. The eye traces the refracted rays backward and therefore perceives the coin at a position higher than its actual position.

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6. Why does the speed of light change during refraction?

The speed of light depends on the medium through which it travels. When light enters a different optical medium, its speed changes. This change in speed can cause the light ray to change direction.

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7. Does the frequency of light change during refraction?

No. The frequency remains unchanged when light passes from one transparent medium to another. The speed and wavelength change.

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8. Why is the power of a convex lens positive?

A convex lens is a converging lens and has a positive focal length under the Cartesian sign convention. Since P = 1/f.

its power is positive.

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9. What is the most important difference between a concave mirror and a concave lens?

A concave mirror is a converging reflecting device, whereas a concave lens is a diverging refracting device.

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10. Why should focal length be converted into metres while calculating lens power?

Because the standard unit of lens power, the dioptre, is defined using focal length in metres: P = 1/f (where f is measured in metres).

Therefore, a focal length given in centimetres must first be converted into metres.

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Conclusion

The chapter Light – Reflection and Refraction becomes much easier when it is understood as a connected system rather than as a collection of formulas.

The central ideas are simple: reflection explains how light bounces from surfaces, while refraction explains how light changes direction when its speed changes between transparent media. From these two phenomena, we can understand the working of spherical mirrors, lenses, image formation, ray diagrams, refractive index, lens power and many everyday optical devices.

For examination preparation, students should pay particular attention to ray diagrams, sign conventions, mirror and lens formulas, magnification, refractive index, power of lenses and the nature of images. Understanding why an image is formed at a particular position is much more useful than memorising isolated cases.