Question

A single-slit diffraction pattern is formed on a distant screen. Assuming the angles involved are small, by what factor will the width of the central bright spot on the screen change if the slit width is doubled

Answer 1

y ’= y / 2

thus when the slit width is doubled the pattern width is halved

Step-by-step explanation:

The diffraction of a slit is given by the expressions

a sin θ = m λ

where a is the width of the slit, λ is the wavelength and m is an integer that determines the order of diffraction.

sin θ = m λ / a

If this equation

a ’= 2 a

we substitute

2 a sin θ'= m λ

sin θ'= (m λ / a) 1/2

sin θ ’= sin θ / 2

We can use trigonometry to find the width

tan θ = y / L

as the angle is small

tan θ = sin θ / cos θ = sin θ

sin θ = y / L

we substitute

y ’/ L = y/L 1/2

y ’= y / 2

thus when the slit width is doubled the pattern width is halved