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 $(25,25\sqrt{3})$



Finding image for lans:
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
where, $f=30cm,u=-50cm$
so, $v=75cm$
this image will work as a vertual object for mirror.
Now from mirror formula,
$\frac{1}{v}=\frac{1}{f}=\frac{1}{u}$
where, $f=50cm,u=25cm$
So, $v=-50cm$

Taking $cos$ and $sin$ component of this image, because when mirror is rotating by $\theta$ then image rotates by $2\theta .$
So, $50cos{60}^o=2550sin{60}^o=25\sqrt{3}$

then, the distance by lans
$x=50-25=25cm$
and $y=25\sqrt{3}$
So, $(x,y)=(25,25\sqrt{3})$