Question

A diffraction-limited lens can focus light to a 10$\mu m$diameter spot on a screen. Do the following actions make the spot diameter larger, make it smaller, or leave it unchanged?

A. Decreasing the wavelength of the light.

B. Decreasing the lens diameter.

C. Decreasing the lens focal length.

D. Decreasing the lens-to-screen distance.

Short answer

(A) Decrease

(B) Increase

(C) Decrease

(D) Increase

Step-by-step solution

Part A).Step.1 Given Information 

Decreasing the wavelength of the light.

Part A) Step 2.simplify  

since ${\omega }_{min}=\frac{2.44\lambda f}{D}$,hence from this dependence we have

Decreasing $\lambda$decreases$\omega$

Part b).step 1. Given statement

Decreasing the lens diameter

Part b).Step 2.simplify

we know that ${\omega }_{min}\approx \frac{2.44\lambda f}{D}$

Therefore, Decreasing D increases$\omega$

Part C).Step 1.Given statement

Decreasing the lens focal length.

Part C) Step 2.simplify

we have, ${\omega }_{min}\approx \frac{2.44\lambda f}{D}$

Therefore, Decreasing the focal length f will decreases $\omega$

Part D) Step 1.Given Information 

Decreasing the lens-to-screen distance.

Part D) Step 2.simplify 

we know that ${\omega }_{min}\approx \frac{2.44\lambda f}{D}$

Decreasing the lens-to-screen distance means the screen is farther from the focal plane. This mean spot will get larger.