Chapter 23, Problem 63P

To determine

The focal length of the diverging lens which is placed 28 cm behind a 38 cm focal length converging lens given that parallel light strikes the diverging lens and after passing through the converging lens it becomes parallel again.

Answer to Problem 63P

Solution:

Focal length of the diverging lens is -10 cm.

Explanation of Solution

Given:

Distance between the diverging and converging lens is 28 cm and the converging lens has a focal length of 38 cm. Parallel light falls on diverging lens and comes out parallel from the converging lens.

Calculation:

If parallel light falls on the diverging lens, it diverges. If that divergind beam is traced backwards they meet at the focal point of the diverging lens. Only if that focal point is also the focal point of the converging lens then the diverging beam comes out as a parallel beam from converging lens.

This if diverging lens has focal length f₁ and converging lens has focal length f₂.

$f_1=-\left(f_2-d\right)$ where d is the distance between the lenses i.e. 28 cm.

$f_2=\text{38 cm}$

Thus, $f_1=-\text{1}0\text{ cm}$