"Reflection and Refraction of Light"

About

Light — the fastest thing in the universe — obeys precise geometric laws when it encounters surfaces and changes media. This chapter covers the reflection of light by mirrors and the refraction of light through lenses and different media. These principles explain everything from why a straw appears bent in water to how telescopes work.

Key Concepts

20.1 Reflection of Light

Laws of reflection:

1. Incident ray, reflected ray, and normal lie in the same plane
2. Angle of incidence = angle of reflection ($\angle i=\angle r$)

20.2 Spherical Mirrors

Concave mirror: Reflecting surface curved inward. Converging.

Convex mirror: Reflecting surface curved outward. Diverging.

Key parameters:

• Pole (P): Centre of the mirror surface
• Centre of curvature (C): Centre of the sphere
• Radius of curvature (R): Distance PC
• Focus (F): Point where parallel rays converge/diverge from

$f=\frac{R}{2}$

• $f$ depends ONLY on $R$ of the reflecting surface — NOT on the surrounding medium
• A spherical mirror has only ONE focal point
• Plane mirror: $R=\infty$, $f=\infty$

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

Sign convention (Cartesian): Distances measured from pole. Incident light direction = positive.

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

20.3 Refraction of Light

Laws of refraction (Snell's law):

1. Incident ray, refracted ray, and normal lie in the same plane
2. $\frac{\sin i}{\sin r}=\text{constant}=n_{21}$ (refractive index of medium 2 w.r.t. medium 1)

Absolute refractive index: $n=\frac{c}{v}$

20.4 Total Internal Reflection (TIR)

When light travels from denser to rarer medium at an angle greater than the critical angle:

$\sin i_c=\frac{1}{n}$

Applications: Optical fibres, mirage, sparkling diamonds, prism binoculars.

20.5 Lenses

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

Lens maker's formula: $\frac{1}{f}=(n-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$

Power of lens: $P=\frac{1}{f}$ (in dioptres, $f$ in metres)

INTEXT QUESTIONS 20.1

Q1. (a) Which mirror has the largest radius of curvature: plane, concave or convex?

Ans: Plane mirror — it can be thought of as a spherical mirror with infinite radius of curvature. The flatter the mirror, the larger the radius.

(b) Will the focal length of a spherical mirror change when immersed in water?

Ans: No. Focal length depends only on the radius of curvature of the reflecting surface, not on the refractive index of the surrounding medium (unlike lenses).

(c) What is the nature of the image formed by a plane or a convex mirror?

Ans: Both form virtual and erect images. Plane mirror: same size, laterally inverted. Convex mirror: always smaller than the object, behind the mirror.

(d) Why does a spherical mirror have only one focal point?

Ans: Because of the symmetry and geometry of the spherical surface — parallel rays close to the principal axis all converge at (or appear to diverge from) a single point.

Q2. Concave mirrors of radii 5 cm, 7 cm, and 10 cm with common centre of curvature. Calculate focal length for each.

Ans: $f=R/2$

• $R=5$ cm → $f=2.5$ cm
• $R=7$ cm → $f=3.5$ cm
• $R=10$ cm → $f=5.0$ cm

Q3. Radius of curvature of a spherical mirror is 30 cm. What is its focal length if (i) inside surface is silvered? (ii) outside surface is silvered?

Ans: (i) Concave: $f=R/2=15$ cm (ii) Convex: $f=R/2=15$ cm (by sign convention, +15 cm for convex)

Q4. Why are dish antennas curved?

Ans: The parabolic shape reflects parallel incoming signals to a single focal point where the receiver is placed. This concentrates the signal, increases strength, improves clarity, and minimises loss and interference.

Terminal Exercise

1. State the laws of reflection. Derive the mirror formula $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$ for a concave mirror.

2. Define the principal focus of a concave mirror and a convex mirror with ray diagrams.

3. An object is placed 30 cm from a concave mirror of focal length 20 cm. Find the position, nature, and magnification of the image.

4. State the laws of refraction. Define refractive index. Explain why a swimming pool appears shallower than it actually is.

5. What is total internal reflection? State its conditions and give three applications.

6. Derive the lens formula $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$ for a convex lens.

7. A convex lens of focal length 15 cm forms an image 10 cm from the lens. Where is the object placed? Find the magnification.

8. Derive the lens maker's formula. Find the focal length of a plano-convex lens ($n=1.5$, $R=20$ cm).

9. Explain the formation of a rainbow. Why is it always circular?

10. An object is placed 60 cm from a convex lens of focal length 20 cm. Where is the image formed? What is its nature and size?

11. A ray of light passes from air to glass ($n=1.5$) at an angle of incidence 60°. Find the angle of refraction and lateral displacement.

12. Why does a diamond sparkle more than glass?

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