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In Fraunhofer diffraction due to a narrow slit, a screen is placed 2 m 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 Fraunhofer diffraction due to a narrow slit, a screen is placed 2 m...
In the Fraunhofer diffraction pattern due to a single slit of width b, the directions of minima are given by
b sin θ = ±m λ wher n = 12.3.....
or
If θ is measured in radian, than sin θ = 0
θ = mλ/b
b sin θ = ±m λ wher n = 12.3.....
or
If θ is measured in radian, than sin θ = 0
θ = mλ/b
The angular separation θ between the first minimum on either side of the central maximum is
θ = λ/b
Here n = 1
In the given problem, b = 0.2 mm = 0.02 cm
Linear separation between the first minimum and central maximum is as
CP = 5 mm = 0.5 cm
Comparing equation (1) and (2), we get
Most Upvoted Answer
In Fraunhofer diffraction due to a narrow slit, a screen is placed 2 m...
To find the wavelength of light in Fraunhofer diffraction due to a narrow slit, we can use the formula for the location of the minima:
sin(θ) = mλ / a
where θ is the angle of diffraction, m is the order of the minima, λ is the wavelength of light, and a is the slit width.
In this case, we are given that the first minima lie 5 mm on either side of the central maximum. Since the screen is placed 2 m away from the lens, we can use the small angle approximation to simplify the formula:
sin(θ) ≈ tan(θ) = y / L
where y is the distance from the central maximum to the first minima, and L is the distance from the slit to the screen.
Given that y = 5 mm = 0.005 m and L = 2 m, we can substitute these values into the equation to find the angle of diffraction:
θ = tan^(-1)(0.005 / 2)
Next, we can use the formula for the location of the minima to find the wavelength:
sin(θ) = mλ / a
Since the first minima is located on either side of the central maximum, the order of the minima is m = 1. Substituting the values into the equation:
sin(tan^(-1)(0.005 / 2)) = 1λ / 0.2 x 10^(-3)
Simplifying the equation, we can solve for λ:
λ = (0.2 x 10^(-3)) x sin(tan^(-1)(0.005 / 2))
Calculating the value, we find that λ ≈ 5000 nm.
Therefore, the correct answer is option 'B': 5000.
sin(θ) = mλ / a
where θ is the angle of diffraction, m is the order of the minima, λ is the wavelength of light, and a is the slit width.
In this case, we are given that the first minima lie 5 mm on either side of the central maximum. Since the screen is placed 2 m away from the lens, we can use the small angle approximation to simplify the formula:
sin(θ) ≈ tan(θ) = y / L
where y is the distance from the central maximum to the first minima, and L is the distance from the slit to the screen.
Given that y = 5 mm = 0.005 m and L = 2 m, we can substitute these values into the equation to find the angle of diffraction:
θ = tan^(-1)(0.005 / 2)
Next, we can use the formula for the location of the minima to find the wavelength:
sin(θ) = mλ / a
Since the first minima is located on either side of the central maximum, the order of the minima is m = 1. Substituting the values into the equation:
sin(tan^(-1)(0.005 / 2)) = 1λ / 0.2 x 10^(-3)
Simplifying the equation, we can solve for λ:
λ = (0.2 x 10^(-3)) x sin(tan^(-1)(0.005 / 2))
Calculating the value, we find that λ ≈ 5000 nm.
Therefore, the correct answer is option 'B': 5000.
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In Fraunhofer diffraction due to a narrow slit, a screen is placed 2 m 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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