Question:
The source that illuminates the double − slit in 'double - slit interference experiment' emits two distinct monochromatic waves of wavelength 500 nm and 600 nm, each of them producing its own pattern on the screen. At the central point of the pattern when path difference is zero, maxima of both the patterns coincide and the resulting interference pattern is most distinct at the region of zero path difference. But as one moves out of this central region, the two fringe systems are gradually out of step such that maximum due to one wavelength coincides with the minimum due to the other and the combined fringe system becomes completely indistinct. This may happen when path difference in nm is:
The source that illuminates the double − slit in 'double - slit interference experiment' emits two distinct monochromatic waves of wavelength 500 nm and 600 nm, each of them producing its own pattern on the screen. At the central point of the pattern when path difference is zero, maxima of both the patterns coincide and the resulting interference pattern is most distinct at the region of zero path difference. But as one moves out of this central region, the two fringe systems are gradually out of step such that maximum due to one wavelength coincides with the minimum due to the other and the combined fringe system becomes completely indistinct. This may happen when path difference in nm is:
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Need a path difference that is an integer multiple of one wavelength and an odd multiple of half the other wavelength.
Updated On: Nov 4, 2026
- 2000
- 3000
- 1000
- 1500
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The Correct Option is D
Solution and Explanation
Path difference \(\Delta = n\lambda_1 = \left(m + \tfrac12\right)\lambda_2\) with \(\lambda_1 = 500\), \(\lambda_2 = 600\) nm.
Test the options. \(\Delta = 1500\): \(1500/500 = 3\) (maximum of 500 nm) and \(1500/600 = 2.5\) (minimum of 600 nm). It works.
\(\Delta = 1000\): 2 and 1.67, no. \(\Delta = 2000\): 4 and 3.33, no. \(\Delta = 3000\): 6 and 5, both maxima, no.
Answer: (4) 1500
Test the options. \(\Delta = 1500\): \(1500/500 = 3\) (maximum of 500 nm) and \(1500/600 = 2.5\) (minimum of 600 nm). It works.
\(\Delta = 1000\): 2 and 1.67, no. \(\Delta = 2000\): 4 and 3.33, no. \(\Delta = 3000\): 6 and 5, both maxima, no.
Answer: (4) 1500
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