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A double slit of separation 1.5 mm is il...

A double slit of separation 1.5 mm is illuminated by white light (between 4000 and 8000 `Å`). On a screen 120 cm away colored interference pattern is formed. If a pinhole is made on this screen at a distance of 3.0 mm from the central white fringe, some wavelengths will be absent in the transimitted light. Find the second longest wavelength (in `Å`) which will be absent in the transmitted light.

Text Solution

Verified by Experts

The correct Answer is:
5769 `Å`
In a double-slit interference pattern, the distance x of a dark fringe from the central achormatic fringe is
`x = (D)/(2d) (2n + 1 ) (lambda)/(2) , n = 0, 1, 2,…`
`lambda = (75000)/(2n+ 1) Å` (where `n = 0, 1, 2,…)`
Thus, in the range 4000 - 8000 `Å`, the absent wavelength are 6818, 5769, 5800, 4421.
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