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In Franunhofer diffraction due to a narrow slit, a screen is placed 2m away from the lens to obtain the pattern. If the slit width is 0.2 mm and first minima lie 5 mm on either side of the central maximum, find the wavelength of light.
- a)4000
- b)5000
- c)6000
- d)7000
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In Franunhofer diffraction due to a narrow slit, a screen is placed 2m...
In the Fraunhofer diffraction pattern due to a single slit of width b, the directions of minima are given by
If θ is measured in radian, than sin θ = θ
The angular separation θ between the first minimum on either side of the central maximum is
Linear separation between the first minimum and central maximum is as
Comparing equation (1) and (2), we get
If θ is measured in radian, than sin θ = θ
The angular separation θ between the first minimum on either side of the central maximum is
Linear separation between the first minimum and central maximum is as
Comparing equation (1) and (2), we get
Most Upvoted Answer
In Franunhofer diffraction due to a narrow slit, a screen is placed 2m...
Given data:
- Distance between the screen and the lens (L) = 2m
- Width of the slit (a) = 0.2 mm = 0.0002 m
- Distance between the central maximum and the first minima (x) = 5 mm = 0.005 m
Formula:
The position of the minima in a Fraunhofer diffraction pattern due to a narrow slit is given by the formula:
sinθ = λ / a
Calculations:
Let's calculate the angle (θ) for the first minima:
sinθ = λ / a
sinθ = λ / 0.0002
Since the distance between the central maximum and the first minima is given by:
x = L * tanθ
We can rearrange the equation to solve for θ:
θ = atan(x / L)
Substituting the value of x and L:
θ = atan(0.005 / 2)
Now, we can calculate the value of θ:
θ = atan(0.0025) ≈ 0.1431 radians
Since the angle (θ) is very small, we can approximate sinθ ≈ θ:
sinθ ≈ θ ≈ 0.1431
Now, we have the value of sinθ, and we can calculate the wavelength (λ):
λ = a * sinθ
λ = 0.0002 * 0.1431
Result:
The wavelength of light is approximately 0.00002862 meters or 5000 nm.
Therefore, the correct answer is option 'B' (5000).
- Distance between the screen and the lens (L) = 2m
- Width of the slit (a) = 0.2 mm = 0.0002 m
- Distance between the central maximum and the first minima (x) = 5 mm = 0.005 m
Formula:
The position of the minima in a Fraunhofer diffraction pattern due to a narrow slit is given by the formula:
sinθ = λ / a
Calculations:
Let's calculate the angle (θ) for the first minima:
sinθ = λ / a
sinθ = λ / 0.0002
Since the distance between the central maximum and the first minima is given by:
x = L * tanθ
We can rearrange the equation to solve for θ:
θ = atan(x / L)
Substituting the value of x and L:
θ = atan(0.005 / 2)
Now, we can calculate the value of θ:
θ = atan(0.0025) ≈ 0.1431 radians
Since the angle (θ) is very small, we can approximate sinθ ≈ θ:
sinθ ≈ θ ≈ 0.1431
Now, we have the value of sinθ, and we can calculate the wavelength (λ):
λ = a * sinθ
λ = 0.0002 * 0.1431
Result:
The wavelength of light is approximately 0.00002862 meters or 5000 nm.
Therefore, the correct answer is option 'B' (5000).
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In Franunhofer diffraction due to a narrow slit, a screen is placed 2m away from the lens to obtain the pattern. If the slit width is 0.2 mm and first minima lie 5 mm on either side of the central maximum, find the wavelength of light.a)4000b)5000c)6000d)7000Correct answer is option 'B'. Can you explain this answer?
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