Question

A ray of light passes from the vacuum into a medium of refractive index 'n'. If the angle of incidence is twice the angle of refraction, then the angle of incidence in terms of refractive index is

• A. \(sin^{-1}(\frac{n}{2})\)
• B. \(2cos^{-1}(\frac{n}{2})\)
• C. \(2sin^{-1}(\frac{n}{2})\)
• D. \(cos^{-1}(\frac{n}{2})\)

Hint:

Use Snell law and the double angle formula for the sine.

Answer 1

The Correct Option is B

Step 1: Write the ratio
Snell's law gives $n = \frac{\sin i}{\sin r}$ with $i = 2r$, so $\sin i = \sin2r = 2\sin r\cos r$.

Step 2: Direct derivation
$n = \frac{\sin2r}{\sin r} = 2\cos r$, so $r = \cos^{-1}(n/2)$ and $i = 2r$. Option (B).

Final Answer:
2 cos^-1 (n/2). \[ \boxed{\text{(B)}\ 2\cos^{-1}\left(\frac n2\right)} \]