CUET · PHYSICS · PYQ PAPER 2025

The refractive index of water is \( \left(\frac{4}{3}\right) \) and that of glass is \( \left(\frac{3}{2}\right) \).
If the speed of light in glass is \( 2 \times 10^8 \text{ m/s} \), the speed of light in water will be:

A \( \frac{8}{3} \times 10^8 \text{ m/s} \)
B \( 2.4 \times 10^8 \text{ m/s} \)
C \( \left(\frac{9}{4}\right) \times 10^8 \text{ m/s} \)
D \( 1 \times 10^8 \text{ m/s} \)

Verified Solution

Answer & Solution

Correct Answer

(C) \( \left(\frac{9}{4}\right) \times 10^8 \text{ m/s} \)

Step-by-step Solution

Detailed explanation

\( n_w v_w = n_g v_g \) \( v_w = \frac{n_g v_g}{n_w} \) \( v_w = \frac{\left(\frac{3}{2}\right) \times (2 \times 10^8 \text{ m/s})}{\left(\frac{4}{3}\right)} \) \( v_w = \frac{3 \times 10^8 \text{ m/s}}{\frac{4}{3}} = \frac{9}{4} \times 10^8 \text{ m/s} \)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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The refractive index of water is \( \left(\frac{4}{3}\right) \) and that of glass is \( \left(\frac{3}{2}\right) \). If the speed of light in glass is \( 2 \times 10^8 \text{ m/s} \), the speed of light in water will be:

Step-by-step Solution

The refractive index of water is \( \left(\frac{4}{3}\right) \) and that of glass is \( \left(\frac{3}{2}\right) \).
If the speed of light in glass is \( 2 \times 10^8 \text{ m/s} \), the speed of light in water will be: