A ray of light incident on a transparent sphere at an angle π / 4 and refracted at an angle r, emerges from the sphere after suffering one internal reflection. The total angle of deviation of the ray is

Question

A ray of light incident on a transparent sphere at an angle π / 4 and refracted at an angle r, emerges from the sphere after suffering one internal reflection. The total angle of deviation of the ray is (A) (3 π/2)-4 r (B) (π/2)-4 r (C) (π/4)-r (D) (5 π/2)-4 r

Tardigrade Admin · Accepted Answer

According to condition given in question, ray diagram of sphere is

So, deviations are

δ_{1} = \frac{π}{4} - r

δ_{2} = π - 2 r

δ_{3} = \frac{π}{4} - r

Total deviation of light ray is

δ = δ_{1} + δ_{2} + δ_{3} = \frac{3 π}{2} - 4 r

Q. A ray of light incident on a transparent sphere at an angle $π /4$ and refracted at an angle $r$ , emerges from the sphere after suffering one internal reflection. The total angle of deviation of the ray is

$\frac{3 π}{2} - 4 r$

$\frac{π}{2} - 4 r$

$\frac{π}{4} - r$

$\frac{5 π}{2} - 4 r$

According to condition given in question, ray diagram of sphere is

So, deviations are
$δ_{1} = \frac{π}{4} - r$
$δ_{2} = π - 2 r$
$δ_{3} = \frac{π}{4} - r$
Total deviation of light ray is
$δ = δ_{1} + δ_{2} + δ_{3} = \frac{3 π}{2} - 4 r$

Q. A ray of light incident on a transparent sphere at an angle π/4 and refracted at an angle r, emerges from the sphere after suffering one internal reflection. The total angle of deviation of the ray is

23π​−4r

2π​−4r

4π​−r

25π​−4r