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

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