Question

A convex lens and convex mirror are placed co axially and separated by distance $d$. The focal length of both is $20cm$ each. A point object is placed at a distance of $30cm$ from the lens. Then the value of $d$ so that image on the object itself is

Answer 1

Step 1:Given data:

Distance between the convex mirror and convex lens=$d$

The focal length of the convex lens($f_1$) =$20cm$

The focal length of the convex mirror is ($f_2$)=$20cm$

The distance of the image placed from the lens is $u_1$= $-30cm$

The radius of curvature of mirror=$R$

Step 2:Formula applied

According to Lens' formula

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

Step 3:Solution

$\frac{1}{v}-\frac{1}{-30}=\frac{1}{20}$

$$\begin{gathered} \frac{1}{v}=\frac{1}{-30}+\frac{1}{20}=\frac{1}{60} \\ v=60cm \end{gathered}$$

$d+R=v$

$$\begin{gathered} R=2f \\ d+2f=60 \end{gathered}$$

As the focal length of a concave mirror is always negative hence ($f_2=-20cm$)

$d=60-2\left(20\right)=60-40=20cm$

Therefore the distance between the mirror and the lens should be $20cm$ for the path to be retraced.