Question

If the lens diameter is doubled, what happens to the resolvable angle of images produced at fixed wavelength?a. The angle decreases by a factor of two. b. The angle increases by a factor of four. c. The angle stays the same. d. The angle decreases by a factor of four.e. The angle increases by a factor of two.

Answer 1

Answer:

Option A

Explanation:

Angular resolution for any optical equipment can be defined as the ability of that tool to differentiate the smallest details of the image formed.

The angular resolution is given by:

$\theta_{R} = \frac{1.22\lambda}{d}$                   (1)

where

$\theta_{R}$ = Angular Resolution

$\lambda$ = wavelength

d = diameter of the lens

Now,

As per the question:

If the diameter of the lens is doubled, i.e., d' = 2d

Then

From eqn (1):

$\theta'_{R} = \frac{1.22\lambda}{d'} = \frac{1.22\lambda}{2d}$

$\theta'_{R} = \frac{1}{2}\frac{1.22\lambda}{d} = \frac{1}{2}\theta_{R}$

Thus when the diameter is doubled the angular resolution becomes half of its original value.