First slide

The lens

Question

Find the co-ordinates of image of the point object ‘O’ formed after reflection from concave mirror as shown figure assuming prism to be thin and small in size and of prism angle $2^{\circ}$ . Refractive index of the prism material is $\frac{3}{2}$ . Do not consider the refraction of the rays from the prism after reflection from concave mirror.

Moderate

A

$(100 cm, \frac{π}{3} cm)$
B

$(200 cm, \frac{2π}{3} cm)$
C

$(175 cm, \frac{π}{6} cm)$
D

$(150 cm,π cm)$

Solution

When light rays passes through prism, all incident rays will be deviated by the deviation angle given as
$δ = (μ - 1) A = (\frac{3}{2} - 1) 2^{\circ} = 1^{\circ} = \frac{π}{180} rad$
As prism is thin, object and image will be in the same plane as shown in figure. below
Thus in this case the shift of image due to prism in y-direction is given as
Shift $d = a δ = 5 (\frac{π}{180})$
$\Rightarrow d = \frac{π}{36} cm$
Now this image will act as an object for concave mirror. So for mirror formula we use
$u = - 25 cm and f = - 30 cm$
$\Rightarrow \frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
$\Rightarrow v = \frac{u f}{u - f} = 150 cm$
Also, $m = \frac{size of image}{size of object} = \frac{- 150}{- 25} = + 6$
Thus distance of image from principal axis is given as
$= \frac{π}{36} \times 6 = \frac{π}{6} cm$
So co-ordinates of image formed after reflection from concave mirror are $(175 cm, \frac{π}{6} cm)$ .

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