Question

A convex lens of focal length 1.5m is placed in a system of coordinate axis such that its optical centre is at origin and principal axis coinciding with the x-axis. An object and a plane mirror are arranged on the principal axis as shown in figure. Find the value of d (in m) so that y-coordinate of final image (after refraction and reflection) is 0.3m. (Take tan $\theta$ = 0.3)

Answer 1

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$



$\frac{1}{v}-\frac{1}{v}-\frac{1}{-2}=\frac{1}{1.5};v=6m$

$m=\frac{v}{u}=-3$

$x=6-d;tan\theta =\frac{0.3}{x}$

$\Rightarrow d=5m$