Question

Value of critical angle is maximum for light travelling from:

• A. Glass to water
• B. Air to glass
• C. Glass to air
• D. Air to water

Hint:

Critical angle exists only when light travels: \[ \text{Denser Medium} \rightarrow \text{Rarer Medium} \] Smaller refractive index of rarer medium gives larger critical angle.

Answer 1

The Correct Option is C

Concept: Critical angle is defined as the angle of incidence in a denser medium for which the angle of refraction in the rarer medium becomes \(90^\circ\). The relation for critical angle is: \[ \sin C = \frac{n_2}{n_1} \] where:

• \(n_1\) = refractive index of denser medium
• \(n_2\) = refractive index of rarer medium

Critical angle exists only when light travels from denser medium to rarer medium.

Step 1: Understand the condition for critical angle.
Critical angle can occur only when: \[ n_1 > n_2 \] That means light must travel from optically denser medium to optically rarer medium.

Step 2: Analyze each option carefully.

• Glass to water: Possible because glass is denser than water.
• Air to glass: Not possible because light travels from rarer to denser medium.
• Glass to air: Possible and gives very large critical angle because air has very low refractive index.
• Air to water: Not possible because light travels from rarer to denser medium.

Step 3: Compare the critical angles.
For glass to air: \[ \sin C = \frac{1}{1.5} \] For glass to water: \[ \sin C = \frac{1.33}{1.5} \] Since: \[ \frac{1.33}{1.5} > \frac{1}{1.5} \] therefore the critical angle is larger for glass to air. Hence, the correct answer is: \[ \boxed{\text{Glass to air}} \]