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The Fraunhoffer ‘diffraction’ pattern of a single slit is formed in the focal plane of a lens of focal length 1 m. The width of slit is 0.3 mm. If third minimum is formed at a distance of 5 mm from central maximum, then wavelength of light will be
- a)5000 Å
- b)2500 Å
- c)7500 Å
- d)8500 Å
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The Fraunhoffer ‘diffraction’ pattern of a single slit is formed in t...
To find the wavelength of light using the Fraunhoffer diffraction pattern of a single slit, we can use the formula:
λ = (d * sinθ) / m
Where:
- λ is the wavelength of light
- d is the width of the slit
- θ is the angle between the central maximum and the third minimum
- m is the order of the minimum (in this case, m = 3)
Now let's solve the problem step by step.
1. Finding the angle θ:
- The distance from the central maximum to the third minimum is given as 5 mm.
- Since the lens has a focal length of 1 m, we can convert this distance to radians by dividing it by the focal length:
θ = (5 mm) / (1 m) = 0.005 radians
2. Calculating the wavelength:
- The width of the slit is given as 0.3 mm.
- Using the formula, we can substitute the values to find the wavelength:
λ = (0.3 mm * sin(0.005 radians)) / 3
- Converting the width of the slit to meters:
0.3 mm = 0.3 * 10^-3 m
- Substituting the values into the formula:
λ = (0.3 * 10^-3 m * sin(0.005 radians)) / 3
- Simplifying the expression:
λ = 0.1 * 10^-3 m * sin(0.005 radians) / 3
- Evaluating the expression:
λ ≈ 0.033 * 10^-3 m
- Converting the wavelength to Angstroms:
λ ≈ 0.033 * 10^-3 m * 10^10 Å / 1 m
λ ≈ 3300 Å
Therefore, the wavelength of light is approximately 3300 Å, which is closest to option 'A' (5000 Å).
λ = (d * sinθ) / m
Where:
- λ is the wavelength of light
- d is the width of the slit
- θ is the angle between the central maximum and the third minimum
- m is the order of the minimum (in this case, m = 3)
Now let's solve the problem step by step.
1. Finding the angle θ:
- The distance from the central maximum to the third minimum is given as 5 mm.
- Since the lens has a focal length of 1 m, we can convert this distance to radians by dividing it by the focal length:
θ = (5 mm) / (1 m) = 0.005 radians
2. Calculating the wavelength:
- The width of the slit is given as 0.3 mm.
- Using the formula, we can substitute the values to find the wavelength:
λ = (0.3 mm * sin(0.005 radians)) / 3
- Converting the width of the slit to meters:
0.3 mm = 0.3 * 10^-3 m
- Substituting the values into the formula:
λ = (0.3 * 10^-3 m * sin(0.005 radians)) / 3
- Simplifying the expression:
λ = 0.1 * 10^-3 m * sin(0.005 radians) / 3
- Evaluating the expression:
λ ≈ 0.033 * 10^-3 m
- Converting the wavelength to Angstroms:
λ ≈ 0.033 * 10^-3 m * 10^10 Å / 1 m
λ ≈ 3300 Å
Therefore, the wavelength of light is approximately 3300 Å, which is closest to option 'A' (5000 Å).
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Community Answer
The Fraunhoffer ‘diffraction’ pattern of a single slit is formed in t...
A sin θ = n?
ax/f = 3?
(since 6 is very small so sinθ ≈ tanθ ≈ θ = x/f)
or
= 5 x 10-7m = 5000Å
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The Fraunhoffer ‘diffraction’ pattern of a single slit is formed in the focal plane of a lens of focal length 1 m. The width of slit is 0.3 mm. If third minimum is formed at a distance of 5 mm from central maximum, then wavelength of light will bea)5000 Åb)2500 Åc)7500 Åd)8500 ÅCorrect answer is option 'A'. Can you explain this answer?
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