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.

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:

                  (1)

where

= Angular Resolution

= 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):

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

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.