Question

A screen is placed 2m away from the lens to obtain the diffraction pattern in the focal plane of the lens in a single slit diffraction experiment. What will be the slit width if the first minimum lies 5 mm on either side of the central maximum when plane light waves of wavelength 4000 Å are incident on the slit?

(a) 0.16 mm

(b) 0.26 mm

(c) 0.36 mm

(d) 0.46 mm

I have been asked this question by my college professor while I was bunking the class.

This key question is from Fraunhofer Diffraction in division Optics of Engineering Physics II

Answer 1

Correct option is (a) 0.16 mm

For explanation I would say: Given: f = 2 m, x = 5 X 10^-3m, λ = 4 X 10^-7m, n=1

sin θ = \(\frac{nλ}{a}\), we have

a =  \(\frac{n\lambda}{sin⁡\theta} \)

= 1.6 X 10^-4 m

= 0.16 mm.