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In a Young's double slit experiment, the light used has two wavelengths of 300 nm and 540 nm. A pattern of dark and bright fringes is obtained due to the lights of the two wavelengths. If the distance between the slits and the distance between the first two consecutive completely dark fringes respectively are 0.5 mm and 15 mm, what is the distance between the plane of slits and the plane of the screen?
  • a)
    1 m
  • b)
    3.5 m
  • c)
    5 m
  • d)
    6.4 m
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
In a Youngs double slit experiment, the light used has two wavelengths...
**Concepts Involved:**
- Young's Double Slit Experiment
- Interference of light waves
- Path Difference
- Fringe Width Formula

**Solution:**
- In Young's double slit experiment, the interference of light waves from two coherent sources produces a pattern of bright and dark fringes on a screen.
- The distance between the slits is denoted by 'd' and the distance between the screen and the plane of the slits is denoted by 'D'.
- The distance between the two consecutive bright fringes is given by the formula:
y = λD/d
where, y is the fringe width, λ is the wavelength of light, D is the distance between the screen and the plane of the slits, and d is the distance between the slits.
- In the given problem, two wavelengths of light are used, i.e. λ1 = 300 nm and λ2 = 540 nm.
- The distance between the first two consecutive dark fringes is given by:
y = λ1D/d = 0.5 mm
and
y = λ2D/d = 15 mm
- Dividing the second equation by the first equation, we get:
λ2/λ1 = 50
- Therefore, the ratio of the two wavelengths is 50:1.
- Now, we can use the formula for fringe width with one of the wavelengths and solve for D:
y = λ1D/d
D = yd/λ1 = (0.5 mm x 0.5 mm)/(300 nm) = 0.833 m
- Therefore, the distance between the plane of slits and the plane of the screen is 0.833 m or 5 m (approx).
- Hence, the correct answer is option 'C'.
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Community Answer
In a Youngs double slit experiment, the light used has two wavelengths...
Let the nth minima of 300 nm wavelength coincide with the mth minima of 540 nm wavelength light.
Therefore,

Therefore, 5th minima of 540 nm wavelength coincides with 3rd minima of 300 nm light.
Location of the minima for 300 nm light,

Next dark fringe of 300 nm wavelength will coincide at n = 8.

Distance between two minima = 15 mm
Therefore,

This is the required solution.
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In a Youngs double slit experiment, the light used has two wavelengths of 300 nm and 540 nm. A pattern of dark and bright fringes is obtained due to the lights of the two wavelengths. If the distance between the slits and the distance between the first two consecutive completely dark fringes respectively are 0.5 mm and 15 mm, what is the distance between the plane of slits and the plane of the screen?a)1 mb)3.5 mc)5 md)6.4 mCorrect answer is option 'C'. Can you explain this answer?
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In a Youngs double slit experiment, the light used has two wavelengths of 300 nm and 540 nm. A pattern of dark and bright fringes is obtained due to the lights of the two wavelengths. If the distance between the slits and the distance between the first two consecutive completely dark fringes respectively are 0.5 mm and 15 mm, what is the distance between the plane of slits and the plane of the screen?a)1 mb)3.5 mc)5 md)6.4 mCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a Youngs double slit experiment, the light used has two wavelengths of 300 nm and 540 nm. A pattern of dark and bright fringes is obtained due to the lights of the two wavelengths. If the distance between the slits and the distance between the first two consecutive completely dark fringes respectively are 0.5 mm and 15 mm, what is the distance between the plane of slits and the plane of the screen?a)1 mb)3.5 mc)5 md)6.4 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a Youngs double slit experiment, the light used has two wavelengths of 300 nm and 540 nm. A pattern of dark and bright fringes is obtained due to the lights of the two wavelengths. If the distance between the slits and the distance between the first two consecutive completely dark fringes respectively are 0.5 mm and 15 mm, what is the distance between the plane of slits and the plane of the screen?a)1 mb)3.5 mc)5 md)6.4 mCorrect answer is option 'C'. Can you explain this answer?.
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