Two light beams fall on a transparent material block at point 1 and 2 with angle θ 1 and θ 2 ′ respectively, as shown in figure. After refraction, the beams intersect at point 3 which is exactly o

Question

Two light beams fall on a transparent material block at point 1 and 2 with angle $θ_{1}$ and $θ_{2^{'}}$ respectively, as shown in figure. After refraction, the beams intersect at point 3 which is exactly on the interface at other end of the block. Given : the distance between 1 and 2, $d = 43 cm$ and $θ_{1} = θ_{2} = cos^{- 1} (\frac{n _{2}}{2 n _{1}})$ , where refractive index of the block $n_{2} >$ refractive index of the outside medium $n_{1}$ , then the thickness of the block is ________ cm.

Question diagram: Two light beams fall on a transparent material block at poin

Answer:

6.00

Solution:

$n_{1} \times \frac{n _{2}}{2 n _{1}} = n_{2} sin r sin r = \frac{1}{2}$ $r = 3 0^{\circ} tan r = (\frac{d /2}{t}) t = \frac{d}{2 tan r} = \frac{d 3}{2} = \frac{( 4 3 ) 3}{2} = 6 cm$

TestHub · Accepted Answer

​ n 1 ​ × 2 n 1 ​ n 2 ​ ​ = n 2 ​ sin r sin r = 2 1 ​ ​ ​ r = 3 0 ∘ tan r = ( t d /2 ​ ) t = 2 tan r d ​ = 2 d 3 ​ ​ = 2 ( 4 3 ​ ) 3 ​ ​ = 6 cm ​

Physics - Geometrical Optics Question with Solution | TestHub

Doubts & Discussion