A transparent solid cylindrical rod has a ref | vedclass

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

Question

(D) Let the refractive index of the rod be $n = \frac{2}{\sqrt{3}}$.At the point $Q$ on the wall of the rod,the light ray grazes the surface,meaning t

Vedclass · Accepted Answer

$sin^{-1}\left( \frac{1}{\sqrt{3}} \right)$

Vedclass · Answer

(D) Let the refractive index of the rod be $n = \frac{2}{\sqrt{3}}$.At the point $Q$ on the wall of the rod,the light ray grazes the surface,meaning the angle of refraction is $90^{\circ}$. Let $C$ be the critical angle.Using Snell's law at $Q$: $n \sin C = 1 \cdot \sin 90^{\circ} = 1$.$\sin C = \frac{1}{n} = \frac{1}{2/\sqrt{3}} = \frac{\sqrt{3}}{2}$.Thus,$C = 60^{\circ}$.Now,consider the refraction at the point $P$ on the end face. The angle of incidence is $	heta$ and the angle of refraction is $r = 90^{\circ} - C$.Using Snell's law at $P$: $1 \cdot \sin 	heta = n \cdot \sin(90^{\circ} - C) = n \cos C$.Substituting the values: $\sin 	heta = \frac{2}{\sqrt{3}} \cdot \cos 60^{\circ} = \frac{2}{\sqrt{3}} \cdot \frac{1}{2} = \frac{1}{\sqrt{3}}$.Therefore,$	heta = \sin^{-1}\left( \frac{1}{\sqrt{3}} ight)$.

$A$ transparent solid cylindrical rod has a refractive index of $\frac{2}{\sqrt{3}}$. It is surrounded by air. $A$ light ray is incident at the mid-point of one end of the rod as shown in the figure. The incident angle $\theta$ for which the light ray grazes along the wall of the rod is

Similar Questions

$A$ rectangular glass block is placed on a printed paper lying on a horizontal surface. Find the minimum refractive index of the glass for which the letters on the paper are not visible from any of the vertical sides of the block.

The critical angle is $\theta$ for light going from medium $P$ to medium $Q$. If the speed of light in medium $P$ is $V_{P}$,then the speed of light in medium $Q$ is:

$A$ ray of light is incident on the hypotenuse of a right-angled prism after travelling parallel to the base inside the prism. If $\mu$ is the refractive index of the material of the prism,the maximum value of the base angle for which light is totally reflected from the hypotenuse is

Explain the use of optical fibre in the medical field.

Consider telecommunication through optical fibres. Which of the following statements is not true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module