Question

When a ray of light enters a medium of refractive index µ, then it is observed that the angle of refraction is half the angle of incidence. The value of angle of incidence will be ____________.

Options

• 2 sin^-1 (µ/2)

• 2 cos^-1 (µ)

• cos^-1 (µ/2)

• 2 cos^-1 (µ/2)

Answer 1

When a ray of light enters a medium of refractive index µ, then it is observed that the angle of refraction is half the angle of incidence. The value of angle of incidence will be 2 cos^-1 (µ/2).

Explanation:

`mu = "sin i"/("sin"  "r") = "sin i"/("sin" ("i"//2))`

`= (2  "sin" ("i"//2)  "cos" ("i"//2))/("sin"("i"//2))`

`= 2  "cos" ("i"//2) or mu/2 = "cos"  ("i"//2)`

`"or i" = 2  "cos"^-1  (mu//2)`