Question

A convex lens of focal length 1.5 m 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 fig. Find value of d (in m) so that y-coordinate of image (after refraction and reflection) is 0.3 m. (Take $tan\theta =0.3)$

Answer 1

For image formed by refraction through the lens,

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

$⟹\frac{1}{v}-\frac{1}{-2}=\frac{1}{1.5}$

$⟹v=6m$

Magnification M=$\frac{v}{u}=\frac{6}{-2}=-3$

Hence image is formed 0.3 m below the axis.

From the figure,

$x=6-d$

& $\tan \theta =\frac{0.3}{x}$

$⟹x=1m$

$⟹d=5m$