Two identical radiators have a separation of d=λ/4 where λ is the wavelength of the waves emitted by either source. The initial phase difference between the sources is λ/4. Then the intensity on the screen at a distant point situated at an angle θ=30∘ from the radiators is (here I0 is intensity at that point due to one radiator alone)
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a
I0
b
2I0
c
3I0
d
4I0
answer is B.
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Detailed Solution
The intensity at a point on screen is given byI=4I0cos2(ϕ/2)where ϕ is the phase difference. In this problem ϕ arises (i) due to initial phase difference of π/4 and (ii) due to path difference for the observation point situated at θ=30∘. Thusϕ=π4+2πλ(dsinθ)=π4+2πλ⋅λ4sin30∘=π4+π4=π2Thus ϕ2=π4 and I=4I0cos2(π/4)=2I0