1. Light and Its Reflection
Light is a form of energy that enables us to see objects. In a uniform transparent medium, light travels approximately in straight lines. When light strikes a surface and returns into the same medium, the phenomenon is called reflection.
Laws of Reflection
- The angle of incidence is equal to the angle of reflection: ∠i = ∠r.
- The incident ray, reflected ray and normal at the point of incidence lie in the same plane.
reflected ray
/
/ r
/
--------------------•---------------- surface
|\
normal \ i
\
incident ray
Normal: A line perpendicular to the reflecting surface at the point of incidence. Angles of incidence and reflection are measured from the normal, not from the surface.
Regular and Diffuse Reflection
| Regular reflection | Diffuse reflection |
|---|---|
| Occurs on a smooth surface; reflected rays remain orderly. | Occurs on an irregular surface; reflected rays scatter in different directions. |
| Can form a clear image. | Does not generally form a sharp image. |
2. Spherical Mirrors
A spherical mirror is a part of a hollow sphere with a reflecting surface. There are two types:
Concave mirrorReflecting surface is on the inner side of the spherical surface. It is a converging mirror for parallel rays.
Convex mirrorReflecting surface is on the outer side. It is a diverging mirror for parallel rays.
Important Terms
| Term | Meaning |
|---|---|
| Pole (P) | Centre of the reflecting surface of a spherical mirror. |
| Centre of curvature (C) | Centre of the sphere of which the mirror is a part. |
| Radius of curvature (R) | Distance PC. |
| Principal axis | Straight line passing through P and C. |
| Principal focus (F) | Point where parallel rays meet or appear to meet after reflection. |
| Focal length (f) | Distance between pole and principal focus. |
For a spherical mirror: R = 2f
Ray Rules for Concave Mirror
- A ray parallel to the principal axis reflects through F.
- A ray passing through F reflects parallel to the principal axis.
- A ray passing through C retraces its path after reflection.
- A ray directed towards the pole reflects according to the law of reflection.
Ray Rules for Convex Mirror
- A ray parallel to the principal axis appears to diverge from F behind the mirror.
- A ray directed towards F behind the mirror emerges parallel to the principal axis.
- A ray directed towards C behind the mirror appears to retrace its path.
3. Image Formation by Concave Mirror
| Object position | Image position | Nature |
|---|---|---|
| At infinity | At F | Real, inverted, highly diminished (point-sized) |
| 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 |
Image Formation by Convex Mirror
A convex mirror always forms an image behind the mirror between P and F. The image is virtual, erect and diminished.
Use in vehicles: Convex mirrors provide a wider field of view and form erect, diminished images, allowing drivers to see a larger region behind the vehicle.
4. Sign Convention for Spherical Mirrors
For numerical problems, the Cartesian sign convention is used. Take the pole as origin and the principal axis as the x-axis.
- All distances are measured from the pole.
- Distances measured in the direction of incident light are positive.
- Distances measured opposite to the direction of incident light are negative.
- Heights above the principal axis are positive.
- Heights below the principal axis are negative.
Mirror Formula
1/f = 1/v + 1/u
Here u = object distance, v = image distance and f = focal length.
Magnification for Mirror
m = hᵢ/hₒ = -v/u
If m is positive, the image is erect; if m is negative, the image is inverted. |m| greater than 1 indicates an enlarged image; |m| less than 1 indicates a diminished image.
5. Solved Mirror Numericals
Example 1: A concave mirror has f = −15 cm and an object is placed at u = −30 cm. Find v.
1/v = 1/f − 1/u = −1/15 − (−1/30) = −1/30
v = −30 cm. The image forms at C and is real, inverted and same size.
1/v = 1/f − 1/u = −1/15 − (−1/30) = −1/30
v = −30 cm. The image forms at C and is real, inverted and same size.
Example 2: For the same mirror, m = −v/u = −(−30)/(−30) = −1. Thus the image is inverted and same size.
6. Refraction of Light
Refraction is the change in direction of light when it passes obliquely from one transparent medium to another because its speed changes.
What Happens When Light Changes Medium?
| Movement | Typical behaviour |
|---|---|
| Optically rarer → optically denser | Light bends towards the normal and its speed decreases. |
| Optically denser → optically rarer | Light bends away from the normal and its speed increases. |
The frequency of light remains unchanged when it crosses the boundary, while its speed and wavelength change.
Laws of Refraction
- The incident ray, refracted ray and normal at the point of incidence lie in the same plane.
- For a given pair of media, the ratio sin i / sin r is constant.
n₂₁ = sin i / sin r
Refractive Index
n = c/v
Here c is the speed of light in vacuum and v is the speed of light in the medium. A larger refractive index means light travels more slowly in that medium relative to vacuum.
7. Refraction Through a Rectangular Glass Slab
When a ray enters a rectangular glass slab obliquely from air, it bends towards the normal. On emerging into air, it bends away from the normal.
air glass slab air
incident | | emergent
\ | \ | \
\ i | \ r | \
------------\---------|-----\-----------|------------\---->
\ | \ | \
\ | \ | \
normal
Emergent ray is parallel to the incident ray
but is laterally displaced.
The emergent ray is parallel to the incident ray for a parallel-sided slab, although it is shifted sideways. This sideways shift is called lateral displacement.
8. Refraction Through a Lens
A lens is a transparent refracting medium bounded by two surfaces, at least one of which is generally curved.
Convex lensThicker at the centre and thinner at the edges; generally converges parallel rays.
Concave lensThinner at the centre and thicker at the edges; generally diverges parallel rays.
Important Lens Terms
| Term | Meaning |
|---|---|
| Optical centre (O) | Point near the centre through which a ray passes approximately without deviation for a thin lens. |
| Principal axis | Line passing through the optical centre and centres of curvature. |
| Principal focus (F) | Point where parallel rays converge or appear to diverge after refraction. |
| Focal length (f) | Distance OF. |
Ray Rules for Convex Lens
- A ray parallel to the principal axis passes through the principal focus on the other side.
- A ray passing through the optical centre travels approximately undeviated.
- A ray passing through the principal focus emerges parallel to the principal axis.
Ray Rules for Concave Lens
- A ray parallel to the principal axis appears to diverge from the focus on the same side.
- A ray directed towards the focus on the opposite side emerges parallel to the principal axis.
- A ray through the optical centre travels approximately undeviated.
9. Image Formation by Convex Lens
| Object position | Image position | Nature |
|---|---|---|
| At infinity | At F₂ | 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 O and F₁ | Same side as object | Virtual, erect, enlarged |
Concave Lens Image
A concave lens always forms an image between the optical centre and focus on the same side as the object. It is virtual, erect and diminished.
10. Sign Convention and Formulae for Lenses
Use the Cartesian sign convention for lenses. Distances are measured from the optical centre.
- Distances measured in the direction of incident light are positive.
- Distances measured opposite to the direction of incident light are negative.
- Heights above the principal axis are positive.
- Heights below the principal axis are negative.
Lens Formula
1/f = 1/v − 1/u
Magnification
m = hᵢ/hₒ = v/u
Power of a Lens
P = 1/f (when f is in metres)
Unit of power is dioptre (D). A convex lens has positive focal length and positive power; a concave lens has negative focal length and negative power.
1 D = 1 m⁻¹
11. Solved Lens Numericals
Example 1: A convex lens has f = +10 cm and u = −15 cm. Find v.
1/v = 1/f + 1/u = 1/10 − 1/15 = 1/30
v = +30 cm. The image is real and inverted.
1/v = 1/f + 1/u = 1/10 − 1/15 = 1/30
v = +30 cm. The image is real and inverted.
Example 2: A concave lens has f = −20 cm and u = −30 cm.
1/v = 1/f + 1/u = −1/20 − 1/30 = −1/12
v = −12 cm. The image is virtual, erect and diminished.
1/v = 1/f + 1/u = −1/20 − 1/30 = −1/12
v = −12 cm. The image is virtual, erect and diminished.
Example 3: A lens has focal length +0.50 m. Its power is P = 1/0.50 = +2 D.
12. Mirror vs Lens
| Feature | Mirror | Lens |
|---|---|---|
| Main phenomenon | Reflection | Refraction |
| Common types | Concave and convex | Convex and concave |
| Formula | 1/f = 1/v + 1/u | 1/f = 1/v − 1/u |
| Magnification | m = −v/u | m = v/u |
| Power | Not expressed in dioptres in this chapter | P = 1/f (metres) |
13. Formula Bank
Reflection∠i = ∠r
Mirror relationR = 2f
Mirror formula1/f = 1/v + 1/u
Mirror magnificationm = hᵢ/hₒ = −v/u
Refractive indexn = c/v
Snell's lawn₂₁ = sin i/sin r
Lens formula1/f = 1/v − 1/u
Lens magnificationm = hᵢ/hₒ = v/u
Lens powerP = 1/f (f in m)
14. 30 Practice Questions
- State the two laws of reflection.
- Differentiate regular and diffuse reflection.
- Define pole, centre of curvature and principal focus of a spherical mirror.
- What is the relation between radius of curvature and focal length of a spherical mirror?
- Differentiate concave and convex mirrors.
- State the ray rules used for drawing images in a concave mirror.
- State the ray rules used for drawing images in a convex mirror.
- Describe the image formed by a concave mirror when the object is between F and P.
- Why is a convex mirror used as a rear-view mirror?
- State the Cartesian sign convention for spherical mirrors.
- Write the mirror formula.
- Write the expression for magnification of a spherical mirror.
- What is refraction of light?
- What happens to light when it travels from a rarer to a denser medium?
- State the laws of refraction.
- Define refractive index.
- Why does a pencil appear bent when partly immersed in water?
- What is lateral displacement through a glass slab?
- Differentiate convex and concave lenses.
- Define optical centre and principal focus of a lens.
- State the ray rules for a convex lens.
- State the ray rules for a concave lens.
- Describe the image formed by a convex lens when the object is between F and O.
- Describe the image formed by a concave lens.
- Write the lens formula.
- Write the magnification formula for a lens.
- Define power of a lens and state its SI unit.
- What is the power of a convex lens with focal length 0.5 m?
- A mirror has f = −20 cm. Find its radius of curvature.
- Why does light change direction during refraction?
15. CBSE PYQ / PYQ-Based Practice
These questions are based on recurring CBSE concepts and competency-oriented patterns, including image formation, refraction through a glass slab, refractive index and lens power. CBSE competency material explicitly assesses these concepts. citeturn1search0turn1search1
- An object is placed beyond the centre of curvature of a concave mirror. State the position, size and nature of the image.
- Why does a concave mirror form a virtual enlarged image when the object is placed between the pole and focus?
- An object is placed at the centre of curvature of a concave mirror. Explain the image formed.
- Using the mirror formula, calculate the image distance for a concave mirror with f = −20 cm and u = −30 cm.
- A mirror produces an image with magnification −2. Interpret the sign and magnitude of magnification.
- Why is the focal length of a convex mirror positive under the Cartesian convention?
- Explain why a convex mirror provides a wider field of view.
- A ray passes obliquely from air into glass. Explain its change in direction and speed.
- Why does an emergent ray from a rectangular glass slab remain parallel to the incident ray?
- Define refractive index and write its relation with the speed of light.
- The refractive index of glass is 1.5. What does this value indicate about the speed of light in glass compared with vacuum?
- Explain why a coin at the bottom of a water-filled vessel appears raised.
- Draw or describe the ray diagram for an object beyond 2F of a convex lens.
- Describe the image formed by a convex lens when the object is between F and 2F.
- Why does a concave lens always form a virtual, erect and diminished image?
- Calculate the image distance for a convex lens with f = +10 cm and u = −15 cm.
- A lens has focal length −0.25 m. Calculate its power and identify the type of lens.
- A convex lens has power +5 D. Calculate its focal length.
- Differentiate between the mirror formula and lens formula, including their magnification expressions.
- Explain, with a labelled ray-diagram description, how the laws of reflection and refraction are verified experimentally.