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A single slits of width 0.1 mm is illuminated by parallel light of wavelength 6000 A and diffraction bands are observed on a screen 40 cm from the slit. The distance (in mm) of third dark band from the central bright band is :
Correct answer is '7.2'. Can you explain this answer?
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Calculation of the Distance of the Third Dark Band from the Central Bright Band in Diffraction
Given data:
- Width of the single slit, w = 0.1 mm
- Wavelength of the incident light, λ = 6000 Å (6000 x 10^-10 m)
- Distance between the slit and the screen, D = 40 cm = 400 mm
To find: Distance of the third dark band from the central bright band
1. Calculation of Angular Position of the Third Dark Band:
- The angular position of the nth dark band is given by the formula:
sinθ ≈ nλ/w
- For the third dark band, n = 3.
- Rearranging the formula, we get:
θ ≈ sin^(-1)(nλ/w)
- Substituting the values, we have:
θ ≈ sin^(-1)((3 x 6000 x 10^-10 m)/(0.1 x 10^-3 m))
θ ≈ sin^(-1)(0.018)
- Using the small angle approximation, sinθ ≈ θ (for small values of θ):
θ ≈ 0.018
2. Calculation of Distance of the Third Dark Band:
- The distance between consecutive dark or bright bands on the screen can be found using the formula:
y = D x tanθ
- For the third dark band, we substitute θ = 0.018 and D = 400 mm:
y = 400 mm x tan(0.018)
y ≈ 7.2 mm
Therefore, the distance of the third dark band from the central bright band is approximately 7.2 mm.
Given data:
- Width of the single slit, w = 0.1 mm
- Wavelength of the incident light, λ = 6000 Å (6000 x 10^-10 m)
- Distance between the slit and the screen, D = 40 cm = 400 mm
To find: Distance of the third dark band from the central bright band
1. Calculation of Angular Position of the Third Dark Band:
- The angular position of the nth dark band is given by the formula:
sinθ ≈ nλ/w
- For the third dark band, n = 3.
- Rearranging the formula, we get:
θ ≈ sin^(-1)(nλ/w)
- Substituting the values, we have:
θ ≈ sin^(-1)((3 x 6000 x 10^-10 m)/(0.1 x 10^-3 m))
θ ≈ sin^(-1)(0.018)
- Using the small angle approximation, sinθ ≈ θ (for small values of θ):
θ ≈ 0.018
2. Calculation of Distance of the Third Dark Band:
- The distance between consecutive dark or bright bands on the screen can be found using the formula:
y = D x tanθ
- For the third dark band, we substitute θ = 0.018 and D = 400 mm:
y = 400 mm x tan(0.018)
y ≈ 7.2 mm
Therefore, the distance of the third dark band from the central bright band is approximately 7.2 mm.
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A single slits of width 0.1 mm is illuminated by parallel light of wavelength 6000 A and diffraction bands are observed on a screen 40 cm from the slit. The distance (in mm) of third dark band from the central bright band is :Correct answer is '7.2'. Can you explain this answer?
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A single slits of width 0.1 mm is illuminated by parallel light of wavelength 6000 A and diffraction bands are observed on a screen 40 cm from the slit. The distance (in mm) of third dark band from the central bright band is :Correct answer is '7.2'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A single slits of width 0.1 mm is illuminated by parallel light of wavelength 6000 A and diffraction bands are observed on a screen 40 cm from the slit. The distance (in mm) of third dark band from the central bright band is :Correct answer is '7.2'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single slits of width 0.1 mm is illuminated by parallel light of wavelength 6000 A and diffraction bands are observed on a screen 40 cm from the slit. The distance (in mm) of third dark band from the central bright band is :Correct answer is '7.2'. Can you explain this answer?.
A single slits of width 0.1 mm is illuminated by parallel light of wavelength 6000 A and diffraction bands are observed on a screen 40 cm from the slit. The distance (in mm) of third dark band from the central bright band is :Correct answer is '7.2'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A single slits of width 0.1 mm is illuminated by parallel light of wavelength 6000 A and diffraction bands are observed on a screen 40 cm from the slit. The distance (in mm) of third dark band from the central bright band is :Correct answer is '7.2'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single slits of width 0.1 mm is illuminated by parallel light of wavelength 6000 A and diffraction bands are observed on a screen 40 cm from the slit. The distance (in mm) of third dark band from the central bright band is :Correct answer is '7.2'. Can you explain this answer?.
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