Question

A small object is placed $50cm$ to the left of a thin convex lens of focal length $30cm$ . A convex spherical mirror of radius of curvature $100cm$ is placed to the right of the lens at a distance of $50cm$. The mirror is titled such that the axis of the mirror is at a angle $\theta ={30}^{\circ }$ to the axis of the lens, as shown in the figure.
If the origin of the coordinate system is taken to be at the centre of the lens, the coordinates $\left(incm\right)$ of the point $(x,y)$ at which the image is formed are:

• A. $(125/3,25/\sqrt{3})$
• B. $(50-25\sqrt{3},25)$
• C. $(0,0)$
• D. $(25,25\sqrt{3})$

Answer 1

The correct option is D $(25,25\sqrt{3})$

Let final image be at a distance x from the lens to its right and between the lens and the mirror.

$\frac{y}{50-x}=tan{60}^0=\sqrt{3}$

$y+\sqrt{3}x=50\sqrt{3}$

This is satisfied by option A and D.

A and B both option satisfy this,

Size of image > Size of object

$\sqrt{y^2+{(50-x)}^2}sin{30}^0>25sin{30}^0$

$y^2+{(50-x)}^2>625$

Checking option D,

$625\left(3\right)+625=4\left(625\right)>625$

Answer is option D.