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In Young's double slit experiment, if the slit widths are in the ratio 1 : 2, the ratio of the intensities at minima and maxima will be
- a)1 : 2
- b)1 : 3
- c)1 : 4
- d)1 : 9
Correct answer is option 'D'. Can you explain this answer?
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In Youngs double slit experiment, if the slit widths are in the ratio ...
Young's double-slit experiment is a fundamental experiment in optics that demonstrates the wave nature of light. In this experiment, a beam of light is passed through two narrow slits and the resulting interference pattern is observed on a screen. The intensity of the pattern varies depending on the distance from the center of the pattern.
Ratio of Intensities at Minima and Maxima
When the slit widths are in the ratio 1:2, the ratio of the intensities at minima and maxima can be determined using the following steps:
1. Find the Path Difference
The path difference between the two waves can be calculated using the formula:
Δx = d sinθ
Where Δx is the path difference, d is the distance between the two slits, and θ is the angle of diffraction.
2. Calculate the Phase Difference
The phase difference between the two waves can be calculated using the formula:
Δφ = 2πΔx/λ
Where Δφ is the phase difference, Δx is the path difference, and λ is the wavelength of the light.
3. Determine the Intensity
The intensity of the interference pattern can be calculated using the formula:
I = I1 + I2 + 2√(I1 I2) cos(Δφ)
Where I1 and I2 are the intensities of the waves from the two slits.
4. Find the Ratio of Intensities
When the slit widths are in the ratio 1:2, the ratio of the intensities at minima and maxima can be calculated using the following formula:
I(min)/I(max) = (1 + √2)/(1 - √2)²
Simplifying this equation gives:
I(min)/I(max) = 1/9
Therefore, the correct answer is option D, 1:9.
Ratio of Intensities at Minima and Maxima
When the slit widths are in the ratio 1:2, the ratio of the intensities at minima and maxima can be determined using the following steps:
1. Find the Path Difference
The path difference between the two waves can be calculated using the formula:
Δx = d sinθ
Where Δx is the path difference, d is the distance between the two slits, and θ is the angle of diffraction.
2. Calculate the Phase Difference
The phase difference between the two waves can be calculated using the formula:
Δφ = 2πΔx/λ
Where Δφ is the phase difference, Δx is the path difference, and λ is the wavelength of the light.
3. Determine the Intensity
The intensity of the interference pattern can be calculated using the formula:
I = I1 + I2 + 2√(I1 I2) cos(Δφ)
Where I1 and I2 are the intensities of the waves from the two slits.
4. Find the Ratio of Intensities
When the slit widths are in the ratio 1:2, the ratio of the intensities at minima and maxima can be calculated using the following formula:
I(min)/I(max) = (1 + √2)/(1 - √2)²
Simplifying this equation gives:
I(min)/I(max) = 1/9
Therefore, the correct answer is option D, 1:9.
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In Youngs double slit experiment, if the slit widths are in the ratio 1 : 2, the ratio of the intensities at minima and maxima will bea)1 : 2b)1 : 3c)1 : 4d)1 : 9Correct answer is option 'D'. Can you explain this answer?
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