Waves: Topic 9.2: The Nature of Single-Slit Diffraction

Question 1

Outline the diffraction pattern observed when light is incident normally on a single slit

Answer 1

When plane waves are incident normally on a single slit, a diffraction pattern is produced
This is represented as a series of light and dark fringes which show the areas of maximum and minimum intensity

Question 2

Outline features of a single-slit diffraction pattern where the slit width is larger than the wavelength of the light

Answer 2

The features of the single-slit diffraction pattern using monochromatic light are:
A central maximum with a high intensity
Equally spaced subsidiary maxima, successively smaller in intensity and half the width of the central maximum

Question 3

If the laser were to be replaced by a non-laser source emitting white light, what would the single slit diffraction pattern be?

Answer 3

The central maximum would be white
All maxima would be composed of a spectrum (colors of the rainbow)
The shortest wavelength (violet / blue) would appear nearest to the central maximum
The longest wavelength (red) would appear furthest from the central maximum
This means red light is diffracted the most, blue light is diffracted the least.
The fringe spacing would be smaller and the maxima would be wider

Question 4

What is the relationship between angle of diffraction and wavelength?

Answer 4

The angle of diffraction is directly proportional to the wavelength of the light
This means that the width of the bright maxima, or fringe, is also proportional to the wavelength

Question 5

State the size of the fringes produced by red and blue light in single-slit diffraction

Answer 5

Red light – which has the longest wavelength of visible light – will produce a diffraction pattern with wide fringes
Blue light – which has a much shorter wavelength – will produce a diffraction pattern with narrow fringes

Question 6

if the blue laser were to be replaced with a red laser, but with an even narrower slit, what will happen to fringe width and intensity?

Answer 6

If the slit was made narrower:
The intensity would decrease (will cause more intensity fringes to appear, successively decreasing in intensity)
The fringe spacing would be wider (because red light is undergoing greater diffraction angles due to narrower slit)

Question 7

Using different sources of monochromatic light demonstrates that (different colors of spectrum)

Answer 7

Increasing the wavelength increases the width of the fringes

Question 8

The angle of diffraction of the first minima can be found using the equation:

Answer 8

theta equals lambda over b
Where:
θ = the angle of diffraction (radians)
λ = wavelength (m)
b = slit width (m)

Question 9

Explain how the equation shows the relationship between wavelength and fringe width and spacing

Answer 9

This equation explains why red light produces wider maxima
It is because the longer the wavelength, λ, the larger the angle of diffraction, θ.

Question 10

Explain how the equation shows the relationship between slit width and fringe width

Answer 10

It also explains why wider slits cause the maxima to be narrower
It is because the wider the slit, b, the smaller the angle of diffraction, θ

Question 11

For two paths, r1 and r2, travelling parallel to each other at an angle, θ, between the normal and the slit, the path difference will be:

Answer 11

path difference = r1 − r2 = b/2 sinθ