As shown in the figure, a parallel beam of light incidents on the upper part of a prism of angle $1…
As shown in the figure, a parallel beam of light incidents on the upper part of a prism of angle $1.8^{\circ}$ and material of refractive index 1.5. The light emerging out from the prism falls on a concave mirror of radius of curvature $40 \mathrm{~cm}$. This distance of the point from the principal axis of the mirror where the light rays are focussed after reflection from the mirror is
4.76 cm
1.57 mm
3.14 mm
6.28 mm
Solution
Parallel beam is deviated by prism by angle,
$
\begin{aligned}
\delta & =(\mu-1) A=(1.5-1) \times 1.8^{\circ}=0.9^{\circ} \\
& =0.9^{\circ} \times \frac{\pi}{180^{\circ}} \text { radian }
\end{aligned}
$
This beam from prism is also parallel and is converged at a point in focal plane by concave mirror.
Distance,
$
\begin{aligned}
x & =F \times \delta=\frac{R}{2} \times \delta=\frac{20}{2} \times 0.9^{\circ} \times \frac{\pi}{180^{\circ}} \\
& =0.157 \mathrm{~cm}=1.57 \mathrm{~mm}
\end{aligned}
$
