Comprehension
In a Youngβs double slit experiment, each of the two slits A and B, as shown in the figure, are oscillating about their fixed center and with a mean separation of 0.8 mm. The distance between the slits at time t is given by π = (0.8 + 0.04 sin ππ‘) mm, where π = 0.08 rad s β1 . The distance of the screen from the slits is 1 m and the wavelength of the light used to illuminate the slits is 6000 β«. The interference pattern on the screen changes with time, while the central bright fringe (zeroth fringe) remains fixed at point O.
Question: 1
The \(8^{th}\) bright fringe above the point O oscillates with time between two extreme positions. The separation between these two extreme positions, in micrometer (πm), is ______.
The \(8^{th}\) bright fringe above the point O oscillates with time between two extreme positions. The separation between these two extreme positions, in micrometer (πm), is ______.
Updated On: Mar 9, 2025
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Correct Answer: 601.5
Solution and Explanation
Fringe Width Difference Calculation
Step 1: Formula for Fringe Width Difference
The fringe width difference \( \Delta y \) is calculated using the given parameters: \[ \Delta y = \frac{8 \lambda D}{(0.8 - 0.04) \times 10^{-3}} - \frac{8 \lambda D}{(0.8 + 0.04) \times 10^{-3}} \] where:
- \( \lambda \): The wavelength of the light used
- \( D \): The distance between the slits and the screen
- The denominator represents the small variation in slit separation.
Step 2: Substituting Values and Solving
\[ \Delta y = 601.5 \, \mu \text{m} \]
Final Answer:
The fringe width difference due to the variation in slit separation is \( 601.5 \, \mu \text{m} \).
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Question: 2
The maximum speed in πm/s at which the 8th bright fringe will move is __________.
The maximum speed in πm/s at which the 8th bright fringe will move is __________.
Updated On: Mar 9, 2025
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Correct Answer: 24
Solution and Explanation
Amplitude and Maximum Speed of Fringe Oscillation
Step 1: Amplitude of Oscillation
The amplitude of oscillation of the fringe is calculated as: \[ A = \frac{\Delta y}{2} = \frac{601.50 \, \mu \text{m}}{2} \]
Step 2: Maximum Speed of the Oscillation
The maximum speed of the oscillation is given by: \[ v_{\text{max}} = A \omega \] where \( \omega \) is the angular frequency.
Substitute the values:
\[ v_{\text{max}} = 300.75 \, \mu \text{m} \times 0.08 = 24.06 \, \mu \text{m/s} \]
Final Answer:
The maximum speed of the fringe oscillation is \( v_{\text{max}} = 24 \, \mu \text{m/s} \).
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