Question

Suppose that the angle of incidence of plane waves on a double slit with 0.010 mm is β = 20° (instead of the 0° angle we considered in class). If λ = 532 nm, then what angle θ1 does the m = 1 far-field interference fringe make? Hint: You must take into account the path difference for the light rays incident on the slits. [ans. 23.3°]

Answer 1

To do this kind of problems one need to subtract the extra path difference between two coherent sources before incident on slits This extra path difference is given by d sin β where, d is the distance between the slits Then the total path difference between the two interfering rays coming to the screen is dsin θ _ d sin β For first order maximum, this path difference must be equal to wavelength λ . Therefore, one should have, d sin + d sin B 532x109 0.01x103 0.0532 0.3420 - 0.3952 Hence θ = sin-1 (0.3952) - 23.30