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Light source of wavelength 400 nm used i...

Light source of wavelength 400 nm used in a Lloyd's mirror, lies 1 mm above the plane mirror. Find the distance of first minima above the mirror. Distance of the screen from the plane of the sources is 2 m.

Text Solution

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Consider the formation of minimum at point P as shown in figure. Path difference between the rays reaching at point P is
`Deltax=d/2 sin theta=lambda` (for first minimum)

`rArr d xx tan theta approx 2lambda ( sin theta approx tan theta)`
`rArr dxxy/D=2lambda`
`rArr y=D/d(2lambda)`
:. Distance of first minima above the mirror
`Y=2/(2xx10^(-3))xx2xx400xx10^(-9)=0.8mm`
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