Optics: Fringe Shift in the Two-hole Interference Equipment

  • The fringe shift phenomenon
  • Comparison between double hole and double slit patterns

Fringe Shift Phenomenon

  • Occurs when a light source passes through a double hole or double slit setup
  • Resulting interference pattern shows fringe shifts compared to the expected pattern

Double Hole Interference Pattern

  • Two small holes close to each other
  • Light from a single source passes through the holes
  • Interference pattern observed on the screen

Double Slit Interference Pattern

  • Two narrow slits close to each other
  • Light from a single source passes through the slits
  • Interference pattern observed on the screen

Fringe Shifts in Double Hole Setup

  • Fringe shift is observed when one of the holes is covered partially
  • Shift occurs due to change in path length between the source and screen
  • Equation for fringe shift: 𝛿𝑅 = (𝐷/2) * (π‘₯/𝑦)

Example 1:

  • Distance between source and screen (𝐷) = 2 m
  • Distance between holes (𝑑) = 0.1 mm
  • Fringe shift when one hole is covered by a plate (π‘₯) = 0.5 mm
  • Fringe spacing (𝑦) = 2 cm
  • 𝛿𝑅 = (2/2) * (0.5/20) = 0.025 mm

Fringe Shifts in Double Slit Setup

  • Fringe shift occurs due to changes in path difference between the two slits
  • Caused by varying the distance between the slits or changing the angle of incidence of the light

Example 2:

  • Distance between source and screen (𝐷) = 1 m
  • Distance between slits (𝑑) = 0.2 mm
  • Change in distance between the slits (π‘₯) = 0.1 mm
  • Wavelength of light (πœ†) = 600 nm
  • Fringe shift can be calculated using the equation: 𝛿𝑅 = (𝐷 * πœ†) / 𝑑

Example 2 (contd.):

  • 𝛿𝑅 = (1 * 600 * 10^-9) / (0.2 * 10^-3) = 3 * 10^-3 m

Comparison between Double Hole and Double Slit Patterns

  • Fringe shift in double hole pattern depends on the separation between the holes and the position of the obstruction
  • Fringe shift in double slit pattern depends on the separation between the slits and the change in distance between them.

Double Hole Interference Pattern

  • The two holes act as two coherent light sources
  • Constructive and destructive interference patterns observed on the screen
  • Fringes appear as bright and dark bands

Double Slit Interference Pattern

  • The two slits act as two coherent light sources
  • Constructive and destructive interference patterns observed on the screen
  • Fringes appear as bright and dark bands

Factors Affecting Fringe Shift in Double Hole Setup

  • Distance between the holes (𝑑)
  • Distance between source and screen (𝐷)
  • Change in position of the obstruction (π‘₯)
  • Wavelength of light (πœ†)

Factors Affecting Fringe Shift in Double Slit Setup

  • Distance between the slits (𝑑)
  • Distance between source and screen (𝐷)
  • Change in distance between the slits (π‘₯)
  • Wavelength of light (πœ†)

Equations

  • Fringe shift in double hole setup: 𝛿𝑅 = (𝐷/2) * (π‘₯/𝑦)
  • Fringe shift in double slit setup: 𝛿𝑅 = (𝐷 * πœ†) / 𝑑

Example 3:

  • Distance between source and screen (𝐷) = 3 m
  • Distance between holes (𝑑) = 0.05 mm
  • Fringe shift when one hole is covered by a plate (π‘₯) = 0.3 mm
  • Fringe spacing (𝑦) = 1.5 cm
  • 𝛿𝑅 = (3/2) * (0.3/15) = 0.015 mm

Example 4:

  • Distance between source and screen (𝐷) = 2 m
  • Distance between slits (𝑑) = 0.1 mm
  • Change in distance between the slits (π‘₯) = 0.05 mm
  • Wavelength of light (πœ†) = 700 nm
  • 𝛿𝑅 = (2 * 700 * 10^-9) / (0.1 * 10^-3) = 0.014 mm

Applications of Fringe Shift Phenomenon

  • Interference-based measurement techniques
  • Testing optical components and instruments
  • Study of wave properties of light

Limitations of Fringe Shift Phenomenon

  • Requires appropriate setup and conditions
  • Accuracy depends on the resolution of measurement devices
  • Sensitivity to external disturbances such as vibrations

Summary

  • Fringe shift occurs in both double hole and double slit interference setups
  • Factors affecting fringe shift include distance between holes/slit, distance between source and screen, change in position/distance, and wavelength of light
  • Equations can be used to calculate fringe shift
  • Applications include measurement techniques and studying wave properties of light

Optics: Fringe Shift in the Two-hole Interference Equipment

  • Double hole vs double slit pattern comparison

Double Hole Interference Pattern

  • Two small holes close to each other
  • Light from a single source passes through the holes
  • Interference pattern observed on the screen
  • Fringes appear as bright and dark bands
  • Fringe spacing depends on the wavelength of light

Double Slit Interference Pattern

  • Two narrow slits close to each other
  • Light from a single source passes through the slits
  • Interference pattern observed on the screen
  • Fringes appear as bright and dark bands
  • Fringe spacing depends on the wavelength of light

Similarities between Double Hole and Double Slit Patterns

  • Both patterns show interference effects
  • Fringes appear as bright and dark bands
  • Pattern spacing depends on the wavelength of light
  • Can be used to study the wave properties of light

Differences between Double Hole and Double Slit Patterns

  • Double hole pattern has two discrete sources of coherent light
  • Double slit pattern has two parallel slits acting as coherent sources
  • Fringe shifts occur differently in the two setups
  • Double hole pattern has a wider central maximum compared to double slit pattern

Double Hole Interference Pattern

  • Two holes act as two coherent light sources
  • Constructive and destructive interference patterns observed on the screen
  • Central maximum is wider compared to double slit pattern
  • Fringe spacing determined by the separation between the holes and the wavelength of light

Double Slit Interference Pattern

  • Two slits act as two coherent light sources
  • Constructive and destructive interference patterns observed on the screen
  • Central maximum is narrower compared to double hole pattern
  • Fringe spacing determined by the separation between the slits and the wavelength of light

Example 1:

  • Distance between holes (𝑑) in double hole setup = 0.1 mm
  • Distance between slits (𝑑) in double slit setup = 0.2 mm
  • Wavelength of light (πœ†) = 600 nm
  • In double hole setup, the fringe spacing would be greater since the holes are closer together compared to the slits in double slit setup.

Example 2:

  • Consider a single source of light passing through both double hole and double slit setups
  • The interference pattern observed on the screen would be different in terms of fringe spacing and intensity distribution
  • This demonstrates the different behaviors of interference in the two setups and the importance of understanding fringe shifts.

Summary

  • Double hole and double slit patterns show interference effects
  • Double hole pattern has two discrete coherent sources, wider central maximum, and fringe spacing determined by hole separation
  • Double slit pattern has two parallel slits acting as coherent sources, narrower central maximum, and fringe spacing determined by slit separation
  • Understanding the differences and similarities allows us to study the wave properties of light more effectively.