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A convex lens of focal length 40 cm is employed to focus the Fraunhofer diffraction pattern of a single slit of 0.3 mm width. Calculate the linear distance of the first order dark band from the central band (λ = 589nm)?
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A convex lens of focal length 40 cm is employed to focus the Fraunhofe...
Given:
- Focal length of convex lens (f) = 40 cm
- Width of single slit (a) = 0.3 mm = 0.03 cm
- Wavelength of light (λ) = 589 nm = 589 × 10^(-7) cm
To calculate the linear distance of the first order dark band from the central band, we can use the formula:
y = mfλD/a
where,
- y is the linear distance of the dark band from the central band
- m is the order of the dark band (in this case, m = 1 for the first order)
- f is the focal length of the lens
- λ is the wavelength of light
- D is the distance between the slit and the lens
- a is the width of the single slit
Calculating D:
In order to calculate D, we need to consider the lens formula:
1/f = 1/v - 1/u
where,
- v is the image distance
- u is the object distance
For a Fraunhofer diffraction pattern, the object distance u is equal to the focal length f.
So, substituting the values in the lens formula:
1/40 = 1/v - 1/40
Simplifying the equation, we get:
1/v = 1/40 + 1/40
1/v = 2/40
v = 40/2
v = 20 cm
The distance D between the slit and the lens is equal to the image distance v.
D = v = 20 cm
Calculating y:
Now, substituting the given values into the formula:
y = (1)(589 × 10^(-7) cm)(20 cm) / (0.03 cm)
Simplifying the equation, we get:
y = (589 × 10^(-7) cm)(20 cm) / (0.03 cm)
y = 393.33 × 10^(-7) cm
Therefore, the linear distance of the first order dark band from the central band is approximately 3.933 cm.
Conclusion:
The linear distance of the first order dark band from the central band in the Fraunhofer diffraction pattern of a single slit is approximately 3.933 cm.
- Focal length of convex lens (f) = 40 cm
- Width of single slit (a) = 0.3 mm = 0.03 cm
- Wavelength of light (λ) = 589 nm = 589 × 10^(-7) cm
To calculate the linear distance of the first order dark band from the central band, we can use the formula:
y = mfλD/a
where,
- y is the linear distance of the dark band from the central band
- m is the order of the dark band (in this case, m = 1 for the first order)
- f is the focal length of the lens
- λ is the wavelength of light
- D is the distance between the slit and the lens
- a is the width of the single slit
Calculating D:
In order to calculate D, we need to consider the lens formula:
1/f = 1/v - 1/u
where,
- v is the image distance
- u is the object distance
For a Fraunhofer diffraction pattern, the object distance u is equal to the focal length f.
So, substituting the values in the lens formula:
1/40 = 1/v - 1/40
Simplifying the equation, we get:
1/v = 1/40 + 1/40
1/v = 2/40
v = 40/2
v = 20 cm
The distance D between the slit and the lens is equal to the image distance v.
D = v = 20 cm
Calculating y:
Now, substituting the given values into the formula:
y = (1)(589 × 10^(-7) cm)(20 cm) / (0.03 cm)
Simplifying the equation, we get:
y = (589 × 10^(-7) cm)(20 cm) / (0.03 cm)
y = 393.33 × 10^(-7) cm
Therefore, the linear distance of the first order dark band from the central band is approximately 3.933 cm.
Conclusion:
The linear distance of the first order dark band from the central band in the Fraunhofer diffraction pattern of a single slit is approximately 3.933 cm.
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A convex lens of focal length 40 cm is employed to focus the Fraunhofe...
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A convex lens of focal length 40 cm is employed to focus the Fraunhofer diffraction pattern of a single slit of 0.3 mm width. Calculate the linear distance of the first order dark band from the central band (λ = 589nm)?
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A convex lens of focal length 40 cm is employed to focus the Fraunhofer diffraction pattern of a single slit of 0.3 mm width. Calculate the linear distance of the first order dark band from the central band (λ = 589nm)? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A convex lens of focal length 40 cm is employed to focus the Fraunhofer diffraction pattern of a single slit of 0.3 mm width. Calculate the linear distance of the first order dark band from the central band (λ = 589nm)? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A convex lens of focal length 40 cm is employed to focus the Fraunhofer diffraction pattern of a single slit of 0.3 mm width. Calculate the linear distance of the first order dark band from the central band (λ = 589nm)?.
A convex lens of focal length 40 cm is employed to focus the Fraunhofer diffraction pattern of a single slit of 0.3 mm width. Calculate the linear distance of the first order dark band from the central band (λ = 589nm)? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A convex lens of focal length 40 cm is employed to focus the Fraunhofer diffraction pattern of a single slit of 0.3 mm width. Calculate the linear distance of the first order dark band from the central band (λ = 589nm)? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A convex lens of focal length 40 cm is employed to focus the Fraunhofer diffraction pattern of a single slit of 0.3 mm width. Calculate the linear distance of the first order dark band from the central band (λ = 589nm)?.
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