A light ray passes from a vacuum into a medium of refractive index n. The angle of refraction is found to be half the angle of incidence. The angle of incidence is ______.

Question

KollegeApply · Accepted Answer

A light ray passes from a vacuum into a medium of refractive index n. The angle of refraction is found to be half the angle of incidence. The angle of incidence is bbunderline(2cos^-1 (n/2)). Explanation: Given: Light is passing from a vacuum to a medium of refractive index n. Angle of refraction, r = i/2 Apply Snell’s law: sin i = n sin(i/2) Use identity: sin i = 2 sin(i/2) cos(i/2) Substitute: `2 sin(i/2) cos(i/2) = n sin(i/2) Cancel sin⁡(i/2) from both sides: $\Rightarrow$ 2 cos(i/2) = n $\Rightarrow$ cos(i/2) = n/2 $\Rightarrow$ cos^-1(n/2) $\Rightarrow$ i = 2 cos^-1(n/2)`

AChoose Your Answer