Chapter 23, Problem 23Q

To determine

To Explain:

That the light rays are said to be reversible in consistent with the thin lens equation.

Answer to Problem 23Q

Solution:

Light rays are said to be reversible and is in consistent with the thin lens equation.

Explanation of Solution

The thin lens equation that relates the image distance to the object distance and the focal length of a thin lens, is given by

$\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}$

Where,

d₀ is the object distance

d_i is the image distance

f is the focal length of the lens

This equation is valid for both converging and diverging lenses, and for all situations, if we use the proper sign conventions.

This equation will make the determination of image position quicker and more accurate than doing ray tracing.

It is obvious from the above equation that, if image position and the object position are interchanged, the equation still holds good.

This can be explained by a ray diagram below.

In the above diagram, the object OO^’ produces an image at II^’. The image distance d_i and the object distance d_o and the focal length satisfy the above equation.

Suppose, if the object is kept in the image position ( at II^’), the image is formed at the object position ( at OO^’). Even if the image and the object distances are changed the equation still satisfy as that of the previous one.

Hence, the object position and the image position are interchangeable and the light rays are reversible.