9.2.2 Intensity of Interference Maxima & Minima

• Using different sources of monochromatic light demonstrates that:
  • Increasing the wavelength increases the width of the fringes
• The angle of diffraction of the first minima can be found using the equation:

• Where:
  • θ = the angle of diffraction (radians)
  • λ = wavelength (m)
  • b = slit width (m)

• This equation explains why red light produces wider maxima
  • It is because the longer the wavelength, λ, the larger the angle of diffraction, θ
• It also explains the coloured fringes seen when white light is diffracted
  • It is because red light (longer λ) will diffract more than blue light (shorter λ)
  • This creates fringes which are blue nearer the centre and red further out

• 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

Slit width and angle of diffraction are inversely proportional. Increasing the slit width leads to a decrease in angle of diffraction, hence the maxima appear narrower

Single Slit Geometry

• The diffraction pattern made by waves passing through a slit of width b can be observed on a screen placed a large distance away

The geometry of single-slit diffraction

• If the distance, D, between the slit and the screen is considerably larger than the slit width, :
  • The light rays can be considered as a set of plane wavefronts that are parallel to each other

Determining the path difference using two parallel waves

• 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:

path difference = r₁ − r₂ = 

• For a minima, or area of destructive interference:

The path difference must be a half-integral multiple of the wavelength

path difference = 

• Equating these two equations for path difference:

• Where n is a non-zero integer number, n = 1, 2, 3...

• Since the angle θ is small, the small-angle approximation may be used:

• Therefore, the first minima, n = 1, occurs at:

• This leads to the equation for angle of diffraction of the first minima:

Step 1: Write down the equation for the angle of diffraction

• • The width of the fringe is related to the size of the angle of diffraction, θ

Step 2: Use the equation to determine the factors that could increase the width of each fringe

Change 1

• • The angle of diffraction, θ, is inversely proportional to the slit width, b

• • Therefore, reducing the slit width would increase the fringe width

Change 2

• • The angle of diffraction, θ, is directly proportional to the wavelength, λ

• • Therefore, increasing the wavelength of the light would increase the fringe width

Change 3

• • The distance between the slit and the screen will also affect the width of the central fringe
  • A larger distance means the waves must travel further hence, will spread out more
  • Therefore, moving the screen further away would increase the fringe width