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KCET · Physics · Ray Optics

The critical angle for a monochromatic light going from medium A to medium B is \(\theta\). If the speed of light in medium A is \(V\), then the speed of light in medium B is

  1. A \(V(1 - \cos\theta)\)
  2. B \(\dfrac{V}{\cos\theta}\)
  3. C \(\dfrac{V}{\sin\theta}\)
  4. D \(V(1 - \sin\theta)\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\dfrac{V}{\sin\theta}\)

Step-by-step Solution

Detailed explanation

Using Snell's law for the critical angle when light travels from medium A to medium B:

\(\mu_A \sin\theta = \mu_B \sin 90^\circ\)

\(\sin\theta = \dfrac{\mu_B}{\mu_A}\)

Since the refractive index of a medium is inversely proportional to the speed of light in that medium, \(\mu = \dfrac{c}{v}\)

\(\dfrac{\mu_B}{\mu_A} = \dfrac{v_A}{v_B}\)

Given the speed of light in medium A is \(v_A = V\)

\(\sin\theta = \dfrac{V}{v_B}\)

\(v_B = \dfrac{V}{\sin\theta}\)

Answer: \(\dfrac{V}{\sin\theta}\)