Two light beams fall on a transparent material block at point 1 and 2 with angle $\theta_1$ and $\theta_{2^{\prime}}$ 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…

Question

Two light beams fall on a transparent material block at point 1 and 2 with angle $\theta_1$ and $\theta_{2^{\prime}}$ 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, $\mathrm{d}=4 \sqrt{3} \mathrm{~cm}$ and $\theta_1=\theta_2=\cos ^{-1}\left(\frac{\mathrm{n}_2}{2 \mathrm{n}_1}\right)$, where refractive index of the block $\mathrm{n}_2 \gt $ refractive index of the outside medium $\mathrm{n}_1$, then the thickness of the block is ________ cm.

Aicharya · Accepted Answer

$\begin{aligned} & n_1 	imes \frac{n_2}{2 n_1}=n_2 \sin r \ & \sin r=\frac{1}{2}\end{aligned}$ $\begin{aligned} & r=30^{\circ} \ & 	an r=\left(\frac{d / 2}{t}ight) \ & t=\frac{d}{2 	an r}=\frac{d \sqrt{3}}{2}=\frac{(4 \sqrt{3}) \sqrt{3}}{2} \ & =6 \mathrm{~cm}\end{aligned}$

Two light beams fall on a transparent material block at point 1 and 2 with angle \(\theta_1\) and…

Solution