Question

Consider a light ray travelling in air is incident into a medium of refractive index `sqrt(2"n")`. The incident angle is twice that of refracting angle. Then, the angle of incidence will be ______.

Options

• `sin^-1(sqrt"n")`

• `cos^-1(sqrt("n"/2))`

• `sin^-1(sqrt(2"n"))`

• `2cos^-1(sqrt("n"/2))`

Answer 1

Consider a light ray travelling in air is incident into a medium of refractive index `sqrt(2"n")`. The incident angle is twice that of refracting angle. Then, the angle of incidence will be `underlinebb(2cos^-1(sqrt("n"/2)))`.

Explanation:

Let 2i be angle of incidence

By Snell's law

⇒ 1 sin 2i = `sqrt(2"n")` sin i

⇒ 2 sin i cos i = `sqrt(2"n")` sin i 

⇒ cos i = `sqrt("n"/2)`

⇒ i = cos^-1 `(sqrt("n"/2))`

⇒ 2i = 2cos^-1 `(sqrt("n"/2))`