Optics Question 884

Question: The box of a pin hole camera, of length L, has a hole of radius a. It is assumed that when the hole is illuminated by a parallel beam of light of wavelength λ the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size (saybmin) when :

Options:

A) a=λL and bmin=4λL

B) a=λ2L and bmin=4λL

C) a=λ2L and bmin=(2λ2L)

D) a=λ1 and bmin=(2λ2L)

Show Answer

Answer:

Correct Answer: A

Solution:

[a] Given geometrical spread=a Diffraction spread =λa×L=λLa

The sum b=a+λLa

For b to be minimum dbda=0dda(a+λLa)=0a=λL

bmin=λL+λL=2λL=4λL



NCERT Chapter Video Solution

Dual Pane