Question

33. A ray of light in air is incident on an equilateral glass prism at an angle i to the normal. After refraction, the light travelled parallel to the base of prism and emerged in air at an angle c to the normal. If the angle between the incident and the emergent rays is 60°, then the refractive index of glass with respect to air is (1) 1.33 (2) 1.5 (3) 1.73 (4) 1.66

Answer 1

Answer:

(3) 1.73

is right answer your questions

Answer 2

Given:

A ray of light in air is incident on an equilateral glass prism. After refraction, the light travelled parallel to the base of prism and emerged in air. The angle between the incident and the emergent rays is 60°.

To find:

Refractive Index of glass (prism) w.r.t air.

Calculation:

Since the ray after 1st refraction travels parallel to the base of the prism, we can say that it is a case of minimum deviation.

Let A be angle of prism:

$\sf{ \therefore \: \mu = \dfrac{ \sin( \dfrac{A + \delta_{min}}{2} ) }{ \sin (\dfrac{A}{2}) } }$

$\sf{ = > \: \mu = \dfrac{ \sin( \dfrac{60 + 60}{2} ) }{ \sin(\dfrac{60}{2}) } }$

$\sf{ = > \: \mu = \dfrac{ \sin( \dfrac{120}{2} ) }{ \sin(\dfrac{60}{2}) } }$

$\sf{ = > \: \mu = \dfrac{ \sin( 60 ) }{ \sin(30) } }$

$\sf{ = > \: \mu = \dfrac{ \dfrac{( \sqrt{3} }{2}) }{ (\dfrac{1}{2} )} }$

$= > \: \mu = \sqrt{3}$

$= > \: \mu = 1.73$

So, final answer is :

Refractive Index of prism glass is 1.73 (Option 3)