In YDSE , the slits have different widths. As a result, the amplitude of waves from two slits is A and 2 A respectively. If I 0 be the maximum intensity of the interference pattern then the intensity of the pattern at a point where the phase difference between waves is ϕ is given by I 0 P 5 + 4 cos ⁡ ϕ . Where P is in integer. Find the value of P?

Question

In YDSE , the slits have different widths. As a result, the amplitude of waves from two slits is A and 2 A respectively. If I 0 be the maximum intensity of the interference pattern then the intensity of the pattern at a point where the phase difference between waves is ϕ is given by I 0 P 5 + 4 cos ⁡ ϕ . Where P is in integer. Find the value of P?, 9, 3, 6, 1

MARKS App · Accepted Answer

As the amplitudes are A and 2 A then the ratio of intensities is 1:4 I m a x = I 0 = I 1 + I 2 + 2 I 1 × I 2 = I + 4 I + 2 × 2 I I 0 = 9 I ⇒ I = I 0 9 Intensity at any point: I ' = I 1 + I 2 + 2 I 1 × I 2 cos ϕ I ' = I + 4 I + 2 I × 4 I cos ϕ I ' = 5 I + 4 I cos ϕ ; I ' = I 5 + 4 cos ϕ I ' = I 0 9 5 + 4 cos ϕ = I 0 P 5 + 4 cos ϕ P = 9

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