Question

A slit of width 'a' is illuminated by white light.
For what value of 'a' will the first minimum
for red light of wavelength 650 nm be at
0 = 15° ? (Given sin 15° = 0.2588)
(A) 4.5 um
(C) 10 um
(B) 2.5 um
(D) 5 um​

Answer 1

Explanation:

please follow me ♥️

Answer 2

Given:

A slit of width 'a' is illuminated by white light.

To find:

For what value of 'a' will the first minimum  for the red light of wavelength 650nm be at  $\theta =15$⁰?

Solution:

The position of the nth dark fringe in Fraunhofer diffraction from a single slit is

$asin\theta=n\lambda$

Now, $a=\frac{n\lambda}{\sin\theta}$

or, $a=\frac{1*650*10^{-9}}{\sin15}$  ( for the first minimum, n=1)

or, $a=\frac{650*10^{-9}}{0.2588}$

Therefore, $a=2.5*10^{-6}=2.5$μm.

The value of 'a' will the first minimum  for the red light of wavelength 650 nm be at  $\theta$ = 15° is 2.5μm.