Question
Physics Question on Youngs double slit experiment
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 (say bmin) when :
A
a=Lλ2 and bmin=(L2λ2)
B
a=λL and bmin=(L2λ2)
C
a=λL and bmin=4λL
D
a=Lλ2 and bmin=4λL
Answer
a=λL and bmin=4λL
Explanation
Solution
sinθ=aλ
B=2a+a2Lλ .....(i)
∂a∂B=0
⇒1−a2Lλ=0
⇒a=λL ....(ii)
Bmin=2λL+2λL [By substituting for a from (ii) in (i)]
=4λL
∴ The radius of the spot =214λL=4λL