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Light of wavelength 6.5xx10^(-7)m is mad...

Light of wavelength `6.5xx10^(-7)`m is made incident on two slits 1 mm apart. The distance between third dark fringe and fifth bright fringe on a screen distant 1 m from the slits will be

A

0.325 mm

B

0.65 mm

C

1.625 mm

D

3.25 mm

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The correct Answer is:
To solve the problem of finding the distance between the third dark fringe and the fifth bright fringe in a double-slit interference pattern, we will follow these steps: ### Step 1: Understand the given data - Wavelength of light, \( \lambda = 6.5 \times 10^{-7} \) m - Distance between the slits, \( d = 1 \) mm = \( 1 \times 10^{-3} \) m - Distance from the slits to the screen, \( D = 1 \) m ### Step 2: Determine the formula for the position of bright and dark fringes 1. The position of the \( n \)-th bright fringe is given by: \[ y_b = \frac{n \lambda D}{d} \] 2. The position of the \( n \)-th dark fringe is given by: \[ y_d = \frac{(2n-1) \lambda D}{2d} \] ### Step 3: Calculate the position of the 5th bright fringe For \( n = 5 \): \[ y_b = \frac{5 \lambda D}{d} = \frac{5 \times (6.5 \times 10^{-7}) \times 1}{1 \times 10^{-3}} \] Calculating this: \[ y_b = \frac{5 \times 6.5 \times 10^{-7}}{1 \times 10^{-3}} = 5 \times 6.5 \times 10^{-4} = 3.25 \times 10^{-3} \text{ m} \] ### Step 4: Calculate the position of the 3rd dark fringe For \( n = 3 \): \[ y_d = \frac{(2 \times 3 - 1) \lambda D}{2d} = \frac{5 \lambda D}{2d} = \frac{5 \times (6.5 \times 10^{-7}) \times 1}{2 \times 1 \times 10^{-3}} \] Calculating this: \[ y_d = \frac{5 \times 6.5 \times 10^{-7}}{2 \times 10^{-3}} = \frac{5 \times 6.5 \times 10^{-4}}{2} = 1.625 \times 10^{-3} \text{ m} \] ### Step 5: Calculate the distance between the 5th bright fringe and the 3rd dark fringe Now, we find the distance between the 5th bright fringe and the 3rd dark fringe: \[ \text{Distance} = y_b - y_d = (3.25 \times 10^{-3}) - (1.625 \times 10^{-3}) = 1.625 \times 10^{-3} \text{ m} \] ### Step 6: Convert the distance to mm To convert meters to millimeters: \[ 1.625 \times 10^{-3} \text{ m} = 1.625 \text{ mm} \] ### Final Answer The distance between the third dark fringe and the fifth bright fringe is \( 1.625 \text{ mm} \). ---

To solve the problem of finding the distance between the third dark fringe and the fifth bright fringe in a double-slit interference pattern, we will follow these steps: ### Step 1: Understand the given data - Wavelength of light, \( \lambda = 6.5 \times 10^{-7} \) m - Distance between the slits, \( d = 1 \) mm = \( 1 \times 10^{-3} \) m - Distance from the slits to the screen, \( D = 1 \) m ### Step 2: Determine the formula for the position of bright and dark fringes ...
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DISHA PUBLICATION-WAVE OPTICS-EXERCISE-2 : CONCEPT APPLICATOR
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