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A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young’s double-slit experiment. What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?
- a)1.66 mm
- b)1.86 mm
- c)1.76 mm
- d)1.56 mm
Correct answer is option 'D'. Can you explain this answer?
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A beam of light consisting of two wavelengths, 650 nm and 520 nm, is u...
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A beam of light consisting of two wavelengths, 650 nm and 520 nm, is u...
's double-slit experiment. The distance between the slits is 0.25 mm, and the distance from the slits to the screen is 1.5 m.
To find the distance between adjacent bright fringes, we can use the equation:
d sinθ = mλ
where d is the distance between the slits, θ is the angle between the line from the slits to the bright fringe and the central axis, m is the order of the fringe (1, 2, 3, etc.), and λ is the wavelength of the light.
For the 650 nm wavelength:
d sinθ = mλ
0.25 x 10^-3 m x sinθ = m x 650 x 10^-9 m
sinθ = m x 650 x 10^-9 m / (0.25 x 10^-3 m)
sinθ = m x 2.6 x 10^-3
θ = sin^-1(m x 2.6 x 10^-3)
For the first-order fringe (m = 1):
θ = sin^-1(1 x 2.6 x 10^-3) = 0.149°
The distance between adjacent bright fringes is given by:
y = L tanθ
where L is the distance from the slits to the screen.
For the 650 nm wavelength:
y = 1.5 m x tan(0.149°) = 0.38 mm
For the 520 nm wavelength:
d sinθ = mλ
0.25 x 10^-3 m x sinθ = m x 520 x 10^-9 m
sinθ = m x 520 x 10^-9 m / (0.25 x 10^-3 m)
sinθ = m x 2.08 x 10^-3
θ = sin^-1(m x 2.08 x 10^-3)
For the first-order fringe (m = 1):
θ = sin^-1(1 x 2.08 x 10^-3) = 0.119°
The distance between adjacent bright fringes is given by:
y = L tanθ
For the 520 nm wavelength:
y = 1.5 m x tan(0.119°) = 0.30 mm
Therefore, the distance between adjacent bright fringes for the 650 nm wavelength is 0.38 mm, and for the 520 nm wavelength is 0.30 mm. This shows that the fringes are closer together for the shorter wavelength, which is consistent with the relationship between wavelength and diffraction.
To find the distance between adjacent bright fringes, we can use the equation:
d sinθ = mλ
where d is the distance between the slits, θ is the angle between the line from the slits to the bright fringe and the central axis, m is the order of the fringe (1, 2, 3, etc.), and λ is the wavelength of the light.
For the 650 nm wavelength:
d sinθ = mλ
0.25 x 10^-3 m x sinθ = m x 650 x 10^-9 m
sinθ = m x 650 x 10^-9 m / (0.25 x 10^-3 m)
sinθ = m x 2.6 x 10^-3
θ = sin^-1(m x 2.6 x 10^-3)
For the first-order fringe (m = 1):
θ = sin^-1(1 x 2.6 x 10^-3) = 0.149°
The distance between adjacent bright fringes is given by:
y = L tanθ
where L is the distance from the slits to the screen.
For the 650 nm wavelength:
y = 1.5 m x tan(0.149°) = 0.38 mm
For the 520 nm wavelength:
d sinθ = mλ
0.25 x 10^-3 m x sinθ = m x 520 x 10^-9 m
sinθ = m x 520 x 10^-9 m / (0.25 x 10^-3 m)
sinθ = m x 2.08 x 10^-3
θ = sin^-1(m x 2.08 x 10^-3)
For the first-order fringe (m = 1):
θ = sin^-1(1 x 2.08 x 10^-3) = 0.119°
The distance between adjacent bright fringes is given by:
y = L tanθ
For the 520 nm wavelength:
y = 1.5 m x tan(0.119°) = 0.30 mm
Therefore, the distance between adjacent bright fringes for the 650 nm wavelength is 0.38 mm, and for the 520 nm wavelength is 0.30 mm. This shows that the fringes are closer together for the shorter wavelength, which is consistent with the relationship between wavelength and diffraction.
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A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young’s double-slit experiment. What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?a)1.66 mmb)1.86 mmc)1.76 mmd)1.56 mmCorrect answer is option 'D'. Can you explain this answer?
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A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young’s double-slit experiment. What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?a)1.66 mmb)1.86 mmc)1.76 mmd)1.56 mmCorrect answer is option 'D'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young’s double-slit experiment. What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?a)1.66 mmb)1.86 mmc)1.76 mmd)1.56 mmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young’s double-slit experiment. What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?a)1.66 mmb)1.86 mmc)1.76 mmd)1.56 mmCorrect answer is option 'D'. Can you explain this answer?.
A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young’s double-slit experiment. What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?a)1.66 mmb)1.86 mmc)1.76 mmd)1.56 mmCorrect answer is option 'D'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young’s double-slit experiment. What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?a)1.66 mmb)1.86 mmc)1.76 mmd)1.56 mmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young’s double-slit experiment. What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?a)1.66 mmb)1.86 mmc)1.76 mmd)1.56 mmCorrect answer is option 'D'. Can you explain this answer?.
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