Interference Patterns

• Interference patterns depend on:
  • The?coherent?light incident on the slits
  • The?distance between the slits and the screen?where the interference pattern is observed
  • The?separation between the slits
• In particular:
  • Successive bright fringes are further apart from each other if the wavelength?λ?of the incident light is longer

Difference in the interference pattern of red and blue light. Red light has a longer wavelength than blue light, so the fringes are more spaced out

• • Similarly, bright fringes are more spaced out if the screen is placed further away from the slits
  • If the separation between the slits is increased, instead successive bright fringes are closer to each other

Explaining the Interference Pattern

• Two slits are separated by a length?d, and a screen is placed a distance?D?away

Light rays of wavelength λ incident on two slits a distance s apart interferes and form bright fringes on a screen placed a distance D away from the slits

• When light rays of wavelength?λ?are incident on the two slits:
  • A?central bright fringe?where the two waves have travelled the?same?distance to the screen and their path difference is?zero
  • Another?bright fringe?is formed either side of the central one where the path difference between the waves is??exactly one wavelength
    • This is constructive interference
  • Dark fringes?(an absence of light) are formed where the path difference between the waves is some number of wavelengths?plus half a wavelength
    • This is destructive interference

• Further bright fringes will be located at each position on the screen where the path difference is exactly equal to?n?number of wavelengths?nλ
• For example: 2λ, 3λ, 4λ...Double-Slit Equation

• The separation?s of successive fringes is given by:
• Where:
  • s?= separation between successive fringes on the screen (m)
  • λ?= wavelength of the waves incident on the slits (m)
  • D?= distance between the screen and the slits (m)
  • d?= separation between the slits (m)

• Note that?s?is the separation between two successive bright fringes or two successive dark ones
• The above equation shows that the separation between the fringes will increase if:
  • The wavelength of the incident light increases
  • The distance between the screen and the slits increases
  • The separation between the slits decreases

Dependence of the interference pattern on the separation between the slits. The further apart the slits, the closer together the bright fringes

Step 1: Write down the known quantities

• • d?= 0.40 mm = 4.0 x 10^–4?m
  • D?= 0.50 m
  • s?= 0.50 cm = 5.0 x 10^–3?m

Note that you must convert all lengths into metres (m)

Step 2: Write down the double-slit equation

Step 3: Rearrange the above equation to calculate the wavelength?λ

Step 4: Substitute the numbers into the above equation

λ = 4.0 × 10^–6?m = 4.0 μm

This corresponds to the infrared area of the electromagnetic spectrum