Optics: Fringe Shift in the Two-hole Interference Equipment
- The Two-hole Interference Experiment
- Light passes through two slits
- Interference pattern observed on a screen
- Fringe Shift
- Shifting the position of one of the slits
- Move one slit towards or away from the other
- Causes a change in the interference pattern
- Equation for Fringe Shift
- Δx = βλL / d
- Δx is the fringe shift
- β is the shift factor (dependent on the angle subtended by the source at the screen)
- λ is the wavelength of light
- L is the distance between the slits and the screen
- d is the distance between the slits
- Application
- Use the fringe shift equation to determine:
- Wavelength of light being used
- Distance between the slits
- Useful in experimental setups and measurements
- Example:
- A two-hole interference setup has a fringe shift of 0.2 mm
- The distance between the slits and the screen is 1 meter
- If the wavelength of light used is 600 nm, find the distance between the slits.
- Solution:
- Given:
- Fringe shift (Δx) = 0.2 mm = 0.2 x 10^-3 m
- Wavelength (λ) = 600 nm = 600 x 10^-9 m
- Distance to screen (L) = 1 m
- Distance between slits (d) = ?
- Using the fringe shift equation:
- Δx = βλL / d
- Rearranging the equation for d:
- Plugging in the values:
- d = (2π/θ) λL / Δx
- Substitute π/θ as β (shift factor)
- Calculating the value of d.
- Conclusion:
- The distance between the slits in the two-hole interference setup is determined using the fringe shift equation.
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