Light — Refraction at Plane Surfaces

Introduction

Refraction is the bending of light when it passes from one transparent medium to another. In ICSE Class 10 Physics, you study Snell's law, refractive index, conditions for total internal reflection, and the action of a prism.

Laws of Refraction

1. The incident ray, the refracted ray, and the normal at the point of incidence all lie in the same plane.
2. Snell's Law: The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media.

sin i / sin r = constant = n (refractive index of second medium with respect to first)

Refractive Index

Absolute Refractive Index

n = speed of light in vacuum / speed of light in the medium = c / v

Relative refractive index of medium 2 with respect to medium 1:

n₂₁ = n₂ / n₁ = v₁ / v₂

Key Points

• Light bends towards the normal when going from rarer to denser medium (v decreases).
• Light bends away from the normal when going from denser to rarer medium (v increases).
• Higher refractive index means the medium is optically denser.

Total Internal Reflection (TIR)

Conditions for TIR

1. Light must travel from an optically denser to a rarer medium.
2. The angle of incidence must be greater than the critical angle for that pair of media.

Critical Angle

The angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90°.

sin C = n₂ / n₁ (where n₁ is denser, n₂ is rarer medium)

Examples of TIR

• Mirage in deserts (hot air near ground is rarer).
• Optical fibres (light travels through core by repeated TIR).
• Sparkling of diamonds (high refractive index → low critical angle → multiple TIR).

Refraction Through a Prism

When white light passes through a prism:

1. Deviation — The light bends towards the base of the prism (angle of deviation = δ).
2. Dispersion — White light splits into its constituent colours (VIBGYOR).

Angle of Deviation (δ)

δ = i₁ + i₂ − A

Where i₁ = angle of incidence on first face, i₂ = angle of emergence on second face, A = angle of the prism.

Dispersion of White Light

This happens because the refractive index of glass is highest for violet light and lowest for red light.

Worked Numericals

Example 1: Snell's Law

Light enters from air (n = 1) to water (n = 1.33) at an angle of incidence of 50°. Find the angle of refraction.

Solution: sin i / sin r = n_water / n_air sin 50° / sin r = 1.33 / 1 0.7660 / sin r = 1.33 sin r = 0.7660 / 1.33 = 0.576 r = sin⁻¹(0.576) ≈ 35.2°

Example 2: Critical Angle

Find the critical angle for water-air interface. (n_water = 1.33, n_air = 1)

Solution: sin C = n_air / n_water = 1 / 1.33 = 0.7519 C = sin⁻¹(0.7519) ≈ 48.8°

Common Mistakes and Fixes

ICSE Exam Focus

This chapter carries 6–8 marks. Key topics: Snell's law numericals, refractive index, TIR conditions, prism deviation and dispersion.

Marks Blueprint: Snell's law/Numericals — 3 marks, TIR/Critical angle — 2 marks, Prism (deviation, dispersion) — 3 marks.

Self-Test Questions

1. State Snell's law of refraction. Write the expression for refractive index.

2. Light passes from water (n = 1.33) to glass (n = 1.5). If the angle of incidence in water is 40°, find the angle of refraction in glass.

3. What is total internal reflection? State the two necessary conditions for TIR.

4. Calculate the critical angle for a glass-air interface (n_glass = 1.5).

5. Explain why a diamond sparkles more than a glass imitation.

6. Draw a ray diagram showing dispersion of white light through a prism. Label all colours.