Refractive index of a medium is mu. If the an | vedclass

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

Question

(A) Given, angle of incidence $i = 2r$, where $r$ is the angle of refraction.According to Snell's law, $\mu_1 \sin i = \mu_2 \sin r$.Assuming the ligh

Vedclass · Accepted Answer

$2 \cos ^{-1}\left(\frac{\mu}{2}\right)$

Vedclass · Answer

(A) Given, angle of incidence $i = 2r$, where $r$ is the angle of refraction.According to Snell's law, $\mu_1 \sin i = \mu_2 \sin r$.Assuming the light travels from air $(\mu_1 = 1)$ to a medium with refractive index $\mu_2 = \mu$, we have:$1 \cdot \sin(2r) = \mu \sin r$Using the trigonometric identity $\sin(2r) = 2 \sin r \cos r$, we get:$2 \sin r \cos r = \mu \sin r$Since $\sin r 
eq 0$, we can divide both sides by $\sin r$:$2 \cos r = \mu \implies \cos r = \frac{\mu}{2}$Thus, $r = \cos^{-1}\left(\frac{\mu}{2}ight)$.Since $i = 2r$, the angle of incidence is $i = 2 \cos^{-1}\left(\frac{\mu}{2}ight)$.

Refractive index of a medium is $\mu$. If the angle of incidence is twice that of the angle of refraction, then the angle of incidence is

Similar Questions

The ratio of the thickness of plates of two transparent mediums $A$ and $B$ is $6 : 4$. If light takes equal time in passing through them,then the refractive index of $B$ with respect to $A$ will be:

State Snell's law of refraction.

$A$ glass cube of length $24 \ cm$ has a small air bubble trapped inside. When viewed normally from one face,it is $10 \ cm$ below the surface. When viewed normally from the opposite face,its apparent distance is $6 \ cm$. The refractive index of glass is:

The apparent depth of water in a cylindrical water tank of diameter $2R \ cm$ is reducing at the rate of $x \ cm/minute$ when water is being drained out at a constant rate. The amount of water drained in $c.c./minute$ is: ($n_1 =$ refractive index of air,$n_2 =$ refractive index of water)

Light enters from air into a given medium at an angle of $45^{\circ}$ with the interface of the air-medium surface. After refraction,the light ray is deviated through an angle of $15^{\circ}$ from its original direction. The refractive index of the medium is

Vedclass Test Series

Exam Paper Generator

Online Exam Module