Question

There are two sets of apparatus of youngs double slit experiment. In set a, the phase difference between the two waves emanating from the slits does not change with time, 5 8 whereas in set b, the phase difference between the two waves from the slits changes rapidly with time. What difference will be observed in the pattern obtained on the screen in the two set ups?

Answer 1

Answer:

a) In Set A, as the phase difference between the two waves emanating from the slits does not change with time so alternate bright and dark bands would be seen on the screen as per Young’s double slit experiment as two slits are acting as coherent sources whereas in Set B, the Phase difference changes rapidly with time, the light waves coming out from two independent sources of light will not have any fixed phase relationship and would be incoherent, when this happens, the intensities on the screen will add up and only bright light will be seen.

b) Given: -

The waves emanating from the two slits have the same amplitude A and same wavelength λ

Derivation: -

Let the displacement produced by wave emanating from slit 1 be y1 and from slit 2 be y2

So, we can write,

y1=Acosωt

And,

y2=Acos(ωt+ϕ)