Question

A convex lens of focal length $10\text{cm}$ is placed $30\text{cm}$ in front of a second convex lens also of the same focal length. A plane mirror is placed after the two lenses. Where should a point object be placed in front of the first lens so that it images on to itself ?

• A. $20\text{cm}$
• B. $15\text{cm}$
• C. $30\text{cm}$
• D. $25\text{cm}$

Answer 1

The correct option is A $20\text{cm}$

The convex lenses and the plane mirror are shown in figure. The combination behaves like a concave mirror. Let the distance of the object from the first lens be $x$.
For the ray to retrace its path. It should be incident normally on the plane mirror. From the diagram, we see that for lens $L_2$
$v=\infty ,f=+10\text{cm},u=?$
From the lens equation, we get
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ or $u=-10\text{cm}$
From the diagram, we see that for lens $L_1$
$v=30-10=20\text{cm},f=+10\text{cm},u=-x$
From the lens equations, we get
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ or $\frac{1}{20}-\frac{1}{-x}=\frac{1}{10}$ or $x=20\text{cm}$