Two light beams fall on a transparent material block at point 1 and 2 with angle and , 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 be

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Solution

Q.
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, $d = 4 \sqrt{3}$ 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. [2025]

Ans.
(6)

$n_{1} \sin (90 - θ_{1}) = n_{2} \sin r$

$n_{1} \times \frac{n_{2}}{2 n_{1}} = n_{2} \sin r$

$\sin r = \frac{1}{2} \Rightarrow r = 30 °$

$\tan r = (\frac{d / 2}{t})$

$t = \frac{d}{2 \tan r} = \frac{d \sqrt{3}}{2} = \frac{(4 \sqrt{3}) \sqrt{3}}{2} = 6 cm$

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