When a light ray enters a medium with refract | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) According to Snell's Law,$n_1 \sin i = n_2 \sin r$. Given $n_1 = 1$ (air) and $n_2 = \mu$,we have $\sin i = \mu \sin r$.Given that the angle of re

Vedclass · Accepted Answer

$2 \cos^{-1} (\mu/2)$

Vedclass · Answer

(A) According to Snell's Law,$n_1 \sin i = n_2 \sin r$. Given $n_1 = 1$ (air) and $n_2 = \mu$,we have $\sin i = \mu \sin r$.Given that the angle of refraction $r = i/2$,we substitute this into the equation:$\sin i = \mu \sin(i/2)$.Using the trigonometric identity $\sin i = 2 \sin(i/2) \cos(i/2)$,we get:$2 \sin(i/2) \cos(i/2) = \mu \sin(i/2)$.Assuming $\sin(i/2) 
eq 0$,we can divide both sides by $\sin(i/2)$:$2 \cos(i/2) = \mu$.$\cos(i/2) = \mu/2$.$i/2 = \cos^{-1}(\mu/2)$.Therefore,$i = 2 \cos^{-1}(\mu/2)$.

When a light ray enters a medium with refractive index $\mu$,it is observed that the angle of refraction is half the angle of incidence. The angle of incidence is .........

Similar Questions

Find the refractive index of glass from the given figure,where the refractive index of water is $\mu_w = 4/3$.

The incorrect statement about the refractive index for a pair of media is:

In refraction,light waves are bent on passing from one medium to a second medium because,in the second medium,

Light of wavelength $\lambda$ in air enters a medium of refractive index $\mu$. Two points in this medium,lying along the path of this light,are at a distance $x$ apart. The phase difference between these points is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module