Back to Physics

Refraction of Light at Plane Surfaces

ICSE Grade 10 Physics - Chapter 4

📚 Smart Summary

1. Refraction of Light

Refraction: The bending of light when it passes from one transparent medium to another due to change in speed.

Cause of Refraction: Light travels at different speeds in different media.

Normal: A line perpendicular to the surface at the point of incidence.

Angle of Incidence (i): Angle between incident ray and normal.

Angle of Refraction (r): Angle between refracted ray and normal.

Refraction towards/away from normal: Light bends towards normal when entering denser medium, away from normal when entering rarer medium.

2. Laws of Refraction

First Law: The incident ray, refracted ray, and normal all lie in the same plane.

Second Law (Snell's Law): The ratio of sine of angle of incidence to sine of angle of refraction is constant for a given pair of media. sin i / sin r = constant.

Refractive Index (n): n = sin i / sin r = c/v, where c is speed of light in vacuum and v is speed in medium.

Absolute Refractive Index: Refractive index with respect to vacuum or air.

Relative Refractive Index: ₁n₂ = n₂/n₁ = v₁/v₂.

3. Refractive Index

Definition: Measure of how much light slows down in a medium.

Formula: n = c/v = sin i / sin r.

Optical Density: Materials with higher refractive index are optically denser.

Examples: Refractive index of water ≈ 1.33, glass ≈ 1.5, diamond ≈ 2.42.

Relation: Higher refractive index means light travels slower in that medium.

4. Total Internal Reflection

Critical Angle: The angle of incidence in denser medium for which angle of refraction in rarer medium is 90°.

Total Internal Reflection (TIR): When light traveling from denser to rarer medium is completely reflected back at the interface.

Conditions for TIR: (1) Light must travel from denser to rarer medium. (2) Angle of incidence must be greater than critical angle.

Formula: sin C = 1/n, where C is critical angle and n is refractive index.

Applications: Optical fibers, prisms, mirages, diamonds' sparkle.

5. Applications and Phenomena

Real and Apparent Depth: Objects in water appear raised due to refraction. Apparent depth = Real depth / n.

Twinkling of Stars: Due to atmospheric refraction caused by varying density of air layers.

Mirage: Optical illusion caused by total internal reflection in hot air layers near ground.

Optical Fibers: Use TIR to transmit light signals over long distances for communication.

Principle of Reversibility: The path of light is reversible; incident and refracted rays can be interchanged.

📐 Formulas

Snell's Law: sin i / sin r = n₂/n₁

Relates angles of incidence and refraction

Refractive Index: n = c/v = sin i / sin r

Speed of light in vacuum to speed in medium

Critical Angle: sin C = 1/n

For denser to rarer medium transition

Apparent Depth = Real Depth / n

Objects appear raised when viewed from rarer medium

🎯 Test Your Knowledge

Multiple Choice Questions

1. Refraction of light occurs due to:

2. When light travels from air to glass, it bends:

3. The refractive index of a medium is:

4. The critical angle is the angle of incidence in:

5. Total internal reflection can occur when light travels from:

6. A coin placed in water appears raised because:

7. The refractive index of diamond is 2.42. This means:

8. Optical fibers work on the principle of:

9. Assertion (A): Stars appear to twinkle. Reason (R): Atmospheric refraction causes apparent position of stars to change.

10. The speed of light in a medium of refractive index 1.5 is:

Practice Numericals

Practice Problem 1: Light travels from air into water with an angle of incidence of 60°. If the refractive index of water is 1.33, calculate the angle of refraction (in degrees, approximately).

Practice Problem 2: The critical angle for glass-air interface is 42°. Calculate the refractive index of glass (approximately).

Practice Problem 3: A tank appears to be 3 m deep when viewed from above. If the refractive index of water is 4/3, find the actual depth (in meters).

Practice Problem 4: Light travels in a medium at a speed of 2.5 × 10⁸ m/s. Calculate the refractive index of the medium (take c = 3 × 10⁸ m/s).

Practice Problem 5: The refractive index of diamond is 2.42. Calculate its critical angle (in degrees, approximately).