Question

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 $\mathrm{1.5.}$ The light emerging out from the prism falls on a concave mirror of radius of curvature $40cm$. This distance of the point from the principal axis of the mirror where the light rays are focussed after reflection from the mirror is

• A. 4.76 cm
• B. 1.57 mm
• C. 3.14 mm
• D. 6.28 mm

Answer 1

Answer: (B)

Parallel beam is deviated by prism by angle,
$\delta =(\mu -1)A=(1.5-1)\times 1.8^{\circ }=0.9^{\circ }$
$=0.9^{\circ }\times \frac{\pi }{180^{\circ }}$ radian
This beam from prism is also parallel and is converged at a point in focal plane by concave mirror.

Distance, $x=F\times \delta =\frac{R}{2}\times \delta =\frac{20}{2}\times 0.9^{\circ }\times \frac{\pi }{180^{\circ }}$
$=0.157cm=1.57mm$