The difference of speed of light in the two m | vedclass

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

Question

(C) The speed of light in a medium is given by $v = \frac{c}{\mu}$,where $c$ is the speed of light in vacuum and $\mu$ is the refractive index of the

Vedclass · Accepted Answer

$1.13$

Vedclass · Answer

(C) The speed of light in a medium is given by $v = \frac{c}{\mu}$,where $c$ is the speed of light in vacuum and $\mu$ is the refractive index of the medium.First,calculate the speed of light in medium $B$ $(v_{B})$:$v_{B} = \frac{3 	imes 10^{8}}{1.47} \approx 2.04 	imes 10^{8} \, m/s = 20.4 	imes 10^{7} \, m/s$.Given the difference in speeds $v_{A} - v_{B} = 2.6 	imes 10^{7} \, m/s$,we can find $v_{A}$:$v_{A} = v_{B} + 2.6 	imes 10^{7} = (20.4 + 2.6) 	imes 10^{7} = 23 	imes 10^{7} \, m/s$.Since $v = \frac{c}{\mu}$,we have $\mu = \frac{c}{v}$. Therefore,the ratio of refractive indices is:$\frac{\mu_{B}}{\mu_{A}} = \frac{c/v_{B}}{c/v_{A}} = \frac{v_{A}}{v_{B}}$.Substituting the values:$\frac{\mu_{B}}{\mu_{A}} = \frac{23 	imes 10^{7}}{20.4 	imes 10^{7}} \approx 1.127 \approx 1.13$.

The difference of speed of light in the two media $A$ and $B$ $(v_{A}-v_{B})$ is $2.6 \times 10^{7} \, m/s$. If the refractive index of medium $B$ is $1.47$,then the ratio of refractive index of medium $B$ to medium $A$ is: (Given: speed of light in vacuum $c = 3 \times 10^{8} \, m/s$)

Similar Questions

$A$ ray of light travels from air to water to glass and again from glass to air. The refractive index of water with respect to air is $x$,glass with respect to water is $y$,and air with respect to glass is $z$. Which one of the following is correct?

If ${ }_{i} \mu_{j}$ represents the refractive index when a ray goes from medium $i$ to medium $j$,then the product ${ }_2 \mu_1 \times { }_3 \mu_2 \times { }_4 \mu_3$ is equal to:

Assertion $(A)$: The colour of radiation does not change on passing through different media.
Reason $(R)$: The media do not absorb or emit colours.

Let $\mu_{1}$ and $\mu_{2}$ be the refractive indices of two media. $v_{1}$ and $v_{2}$ are the velocities of light in the media respectively. Which one of the following relations is $TRUE$?

The angle of incidence is found to be twice the angle of refraction when a ray of light passes from vacuum into a medium of refractive index $\mu$. The angle of incidence will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module