Slide 1

  • Topic: Optics - Fringe Shift in the Two-hole Interference
  • Definition: It refers to the shift in the position of fringes caused by introducing a medium between the double slits and the screen.
  • This phenomenon is related to Young’s double slit experiment.

Slide 2

  • Experimental Setup:
    • Young’s double slit experiment involves a coherent light source, a barrier with two small slits, and a screen.
    • The light passes through the slits, creating interference pattern on the screen.
    • The interference pattern consists of bright and dark fringes.

Slide 3

  • Introduction to Fringe Shift:
    • When a medium of refractive index “n” is introduced between the slits and the screen, the path length of the light passing through the medium changes.
    • This causes a shift in the interference pattern.
    • The fringe shift can be calculated using the formula: δ = (μd/λ) * dΔn

Slide 4

  • Explanation of Variables:
    • δ: Fringe shift
    • μ: Order of the fringe
    • d: Distance between the slits
    • λ: Wavelength of light
    • Δn: Change in refractive index between the slits and the screen

Slide 5

  • Interferometer:
    • An interferometer is a device used to measure the fringe shift accurately.
    • It consists of a microscope, a micrometer screw, and a source of monochromatic light.
    • The interferometer helps in determining the fringe shift by observing the relative positions of fringes.

Slide 6

  • Applications of Fringe Shift:
    • Fringe shift in the two-hole interference is used to measure the refractive index of a medium.
    • It is also used in interferometric techniques for precise measurements in various fields such as metrology, astronomy, and physics research.

Slide 7

  • Example:
    • Consider a Young’s double slit experiment with a distance between the slits (d) of 0.1 mm and a monochromatic light of 600 nm wavelength.
    • If a medium with a refractive index of 1.5 is introduced between the slits and the screen, calculate the fringe shift.

Slide 8

  • Solution:
    • Given: d = 0.1 mm = 0.1 × 10^-3 m
    • λ = 600 nm = 600 × 10^-9 m
    • Δn = 1.5
    • Using the formula: δ = (μd/λ) * dΔn
    • Substitute the given values: δ = (1 * 0.1 × 10^-3 / 600 × 10^-9) * 0.1 × 10^-3 * 1.5

Slide 9

  • Solution (contd.):
    • Simplifying the expression: δ ≈ 0.25 μm or 250 nm
    • Therefore, the fringe shift is approximately 0.25 μm or 250 nm.

Slide 10

  • Summary:
    • Fringe shift is the displacement of the interference pattern caused by the introduction of a medium between the slits and the screen.
    • It is calculated using the formula δ = (μd/λ) * dΔn.
    • The fringe shift can be measured using an interferometer.
    • This phenomenon finds applications in measuring refractive index and in various precision measurement techniques.

Slide 11

  • Equipment:
    • Coherent light source
    • Barrier with two small slits
    • Screen
  • The coherent light source produces light waves with a constant phase relationship.
  • The barrier with two small slits allows the light to pass through and create an interference pattern on the screen.

Slide 12

  • Problem: Calculate the fringe shift for a Young’s double slit experiment with a distance between the slits (d) of 0.2 mm, a monochromatic light of 500 nm wavelength, and a medium with a refractive index of 1.75.
  • Solution:
    • Given: d = 0.2 mm = 0.2 × 10^-3 m
    • λ = 500 nm = 500 × 10^-9 m
    • Δn = 1.75
    • Using the formula: δ = (μd/λ) * dΔn

Slide 13

  • Solution (contd.):
    • Substitute the given values: δ = (1 * 0.2 × 10^-3 / 500 × 10^-9) * 0.2 × 10^-3 * 1.75
    • Simplifying the expression: δ ≈ 0.28 μm or 280 nm
  • Therefore, the fringe shift is approximately 0.28 μm or 280 nm.

Slide 14

  • Factors affecting the fringe shift:
    • Change in the refractive index (Δn)
    • Wavelength of light (λ)
    • Distance between the slits (d)

Slide 15

  • Importance of fringe shift:
    • Helps in determining the refractive index of a medium accurately
    • Plays a crucial role in interferometric techniques for precise measurements
    • Provides valuable insights into the behavior of light waves and interference phenomena

Slide 16

  • Interferometer components:
    • Microscope: Allows precise measurement of fringe shift
    • Micrometer screw: Helps in adjusting the interferometer
    • Source of monochromatic light: Generates coherent light for interference

Slide 17

  • Example: A Young’s double slit experiment with a distance between the slits (d) of 0.15 mm is conducted using red light of wavelength 650 nm. Calculate the fringe shift for a medium with a refractive index of 1.6.

Slide 18

  • Solution:
    • Given: d = 0.15 mm = 0.15 × 10^-3 m
    • λ = 650 nm = 650 × 10^-9 m
    • Δn = 1.6
    • Using the formula: δ = (μd/λ) * dΔn

Slide 19

  • Solution (contd.):
    • Substitute the given values: δ = (1 * 0.15 × 10^-3 / 650 × 10^-9) * 0.15 × 10^-3 * 1.6
    • Simplifying the expression: δ ≈ 0.34 μm or 340 nm
  • Therefore, the fringe shift is approximately 0.34 μm or 340 nm.

Slide 20

  • Summary:
    • The equipment used in a Young’s double slit experiment includes a coherent light source, a barrier with two small slits, and a screen.
    • The fringe shift can be calculated using the formula δ = (μd/λ) * dΔn, where μ is the order of the fringe, d is the distance between the slits, λ is the wavelength of light, and Δn is the change in refractive index.
    • Interferometers are utilized to accurately measure the fringe shift.
    • Factors affecting the fringe shift include the change in refractive index, wavelength of light, and distance between the slits.
    • Understanding fringe shift is essential in determining refractive index and for precision measurements in various fields. Note: I apologize for the confusion, but as an AI text-based model, I can only generate plain text responses and cannot directly create slides in markdown format. However, I will provide you with the content for slides 21 to 30 based on the mentioned topic. You can manually convert the content into the required markdown format for your presentation.

Slide 21

  • Fringe Shift with Medium:
    • Introducing a medium between the double slits and the screen causes a shift in the interference pattern.
    • The shift occurs due to the change in the path length of light passing through the medium.
  • Calculation Formula:
    • Fringe shift (δ) = (μd/λ) * dΔn
    • μ: Order of the fringe
    • d: Distance between the slits
    • λ: Wavelength of light
    • Δn: Change in refractive index

Slide 22

  • Determining Fringe Shift:
    • Interferometer: Used to measure fringe shift accurately.
    • It consists of a microscope, a micrometer screw, and a monochromatic light source.
    • Observing the relative positions of fringes helps determine the shift.
  • Importance in Measurements:
    • Accurate measurement of refractive index.
    • Precision measurement techniques in metrology, astronomy, and research.

Slide 23

  • Example:
    • Young’s double slit with d = 0.3 mm, λ = 550 nm, and Δn = 1.8.
    • Calculate the fringe shift for the 3rd order fringe.
  • Solution:
    • Given: d = 0.3 mm = 0.3 × 10^-3 m
    • λ = 550 nm = 550 × 10^-9 m
    • Δn = 1.8, μ = 3
    • Using the formula: δ = (μd/λ) * dΔn

Slide 24

  • Solution (contd.):
    • Substitute values: δ = (3 * 0.3 × 10^-3 / 550 × 10^-9) * 0.3 × 10^-3 * 1.8
    • Simplifying the expression: δ ≈ 0.93 μm or 930 nm.
    • Therefore, the fringe shift is approximately 0.93 μm or 930 nm.

Slide 25

  • Factors Affecting Fringe Shift:
    1. Refractive Index Change (Δn): Directly proportional to the fringe shift.
    2. Wavelength of Light (λ): Inversely proportional to the fringe shift.
    3. Distance between the Slits (d): Directly proportional to the fringe shift.

Slide 26

  • Significance of Fringe Shift:

    • Determining refractive index accurately.
    • Study of wave optics and behaviour of light.
    • Research and development of interferometry techniques.

  • Example:

    • Calculate the fringe shift for a medium with Δn = 2.2, d = 0.25 mm, and λ = 600 nm. The order of the fringe is 5.

Slide 27

  • Solution:
    • Given: d = 0.25 mm = 0.25 × 10^-3 m
    • λ = 600 nm = 600 × 10^-9 m
    • Δn = 2.2, μ = 5
    • Using the formula: δ = (μd/λ) * dΔn

Slide 28

  • Solution (contd.):
    • Substitute values: δ = (5 * 0.25 × 10^-3 / 600 × 10^-9) * 0.25 × 10^-3 * 2.2
    • Simplifying the expression: δ ≈ 0.46 μm or 460 nm.
    • Therefore, the fringe shift is approximately 0.46 μm or 460 nm.

Slide 29

  • Summary:
    • Fringe shift occurs when a medium is introduced between the double slits and the screen.
    • Calculation formula: δ = (μd/λ) * dΔn
    • Interferometers are used to measure fringe shift accurately.
    • Factors affecting fringe shift include Δn, λ, and d.
    • Fringe shift is important in refractive index measurement and precision measurements.

Slide 30

  • Conclusion:

    • Understanding the fringe shift in two-hole interference is important in wave optics.
    • The calculations help in measuring refractive index accurately.
    • The interchange of positions of fringes provides insight into the behavior of light waves.
    • Interferometric techniques utilize fringe shift for various precise measurements.

  • Any Questions?