Question

In an experiment a convex lens of focal length $15cm$ is placed coaxially on an optical bench in front of a convex mirror at a distance of $5cm$ from it. It is found that an object and its image coincide, if the object is placed at a distance of $20cm$ from the lens. The focal length of the convex mirror is:

• A. $27.5cm$
• B. $25.0cm$
• C. $30.5cm$
• D. $20.0cm$

Answer 1

Answer: (A)

for convex lens:

$u=-20cm,f=15cm$

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

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

$\frac{1}{v}=\frac{1}{15}+\left(\frac{1}{-20}\right)$

$v=\frac{-15\times 20}{-20+15}=\frac{300}{5}=60cm$

for mirror:

$u=55cm,f=?$

for the mirror to form image at '0':

$u=R=2f$

$f=\frac{R}{2}=27.5cm$