Question

A concave mirror of focal length $20cm$ and a convex lens of focal length $10cm$ are kept with their optic axis parallel but separated by $0.5mm$ as shown in the figure. The distance between the lens and the mirror is $10cm$. An object of height $3mm$ is placed on the optical axis of the lens at a distance of $15cm$ from the lens. Find the height of the image (in $mm$) formed by the mirror after refraction from the lens.

IMAGE

Answer 1

We know that: $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

For image formed by mirror:

$u_1=-15cm$

(Direction of incident ray is positive)
For image formed by lens:

$\frac{1}{v_1}-\frac{1}{-15}=\frac{1}{10}$

$\Rightarrow v_1=+30cm$

IMAGE

We know that: $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

For image formed by mirror:

$u_1=+20cm$

(Direction of incident ray is positive)

For image formed by mirror:

$\frac{1}{v_2}+\frac{1}{20}=\frac{1}{-20}$

$\Rightarrow v_2=-10cm$

IMAGE

We know that: $M=\frac{v}{u},M=\frac{h_i}{h_o}$

Overall magnification

$M=\left(\frac{v_1}{u_1}\right)\left(\frac{-v_2}{u_2}\right)$

$\Rightarrow M=\left(\frac{30}{-15}\right)(-\frac{-10}{20})$

$\Rightarrow M=-1$

Length of image$=M\times h_o$

Length of image $=(-1)\left(3\right)=-3mm$