Question

A point object is placed at a distance of 15 cm from a convex lens. The image is formed on the other side at a distance of 30 cm from the lens. When a concave lens is placed in contact with the convex lens, the image shifts away further by 30 cm. Calculate the focal lengths of the two lenses.

Answer 1

Let u = object distance from convex lens

= -15 cm

$v_1=$ image distance from convex lens

= 30 cm

$f_1=$ focal length of convex lens.

Now, $\frac{1}{v_1}-\frac{1}{\left(u\right)}=\frac{1}{f_1}$

or, $\frac{1}{f_1}=\frac{1}{30}-\frac{1}{(-15)}=\frac{1}{30}+\frac{1}{15}$

or, $f_1=\frac{30\times 15}{30+15}=\frac{450}{45}$

= 10 cm

Again, let v = image (final) distance from concave lens = + (30 + 30) = + 60 cm

$v_1=$ object distance from concave lens

= + 30 cm

$f_2=$ focal length of concave lens

Now, $\frac{1}{v}-\frac{1}{v_1}=\frac{1}{f_1}$

or $\frac{1}{f_{)}1}=\frac{1}{60}-\frac{1}{30}$

$=\frac{30-60}{60\times 30}=\frac{-30}{60\times 30}$

or, $f_2=-60\text{cm}$

So, the focal length of convex lens is 10 cm and that of concave lens is 60 cm.