Question

(a) What is the minimum width of a single slit (in multiples of λ) that will produce a first minimum for a wavelength λ?

(b) What is its minimum width if it produces 50 minima?
(c) 1000 minima?
a) (a) 1, (b) 50, (c) 1000
b) (a) 2, (b) 25, (c) 500
c) (a) 3, (b) 20, (c) 333
d) (a) 4, (b) 10, (c) 250

Answer 1

The minimum width of a single slit that will produce a first minimum for a wavelength λ is λ. If the single slit produces 50 minima, the minimum width is 100λ/a. For 1000 minima, the minimum width is 1000λ/a.

Step-by-step explanation:

In single slit diffraction, the minimum width of the single slit that will produce a first minimum is given by the formula d = λ/a, where d is the width of the slit, λ is the wavelength of the light, and a is the angle at which the first minimum occurs.

(a) To find the minimum width of the single slit that will produce a first minimum for a wavelength λ, the value of a is given as 1. Therefore, the minimum width of the single slit is λ.

(b) To find the minimum width if it produces 50 minima, we need to find the value of a using the formula a = 2nλ/d, where n is the number of minima and d is the width of the slit. Substituting the values, we get d = 2nλ/a = 2(50)λ/a = 100λ/a.

(c) Similar to (b), the minimum width for 1000 minima would be d = 1000λ/a.