Question

Consider a light ray travelling in air is incident into a medium of refractive index √2n The incident angle is twice that of refracting angle. Then, the angle of incidence will be:

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

Answer 1

Answer: (D)

$2cos^{-1}(\sqrt{\frac{n}{2}})$

Answer 2

In accordance to the law we find,

$1 \times sin θ = \sqrt2n \times sin(\frac{θ}{2})$

$⇒ cos \frac{θ}{2} = \sqrt{\frac{n}{2}}$

$⇒ θ = 2 cos^{-1} (\sqrt{\frac{n}{2}})$

Hence, the correct option is (D) : $2cos^{-1}(\sqrt{\frac{n}{2}})$