JEE Main Physics Class 12 Wave Optics Part 1 Questions

For (A) xP−xQ=(d+2.5) −(d−2.5)=5m
Phase difference Δϕ due to path difference
=

2π

λ

(Δx)=

2π

20

(5)=

π

2

At A,Q is ahead of P by path, as wave emitted by Q reaches before wave emitted by P.
∴ Total phase difference at A

π

2

−

π

2

=0
(due to P being ahead of Q by 90° )
IA=I1+I2+2√I1√I2‌cos‌Δ‌ϕ
=I+I+2√I√I‌cos(0)=4I
For C
Path difference, xQ−xP=5m
Phase difference Δϕ due to path difference
=

2π

λ

(Δx)=

2π

20

(5)=

π

2

Total phase difference at C=

π

2

+

π

2

=π
Inet =I1+I2+2√I1√I2‌cos(Δϕ)
=I+I+2√I√I‌cos(π)=0
For B,
Path difference, xP−xO=0
Phase difference, Δϕ=

π

2

(due to P being ahead of Q by 90° )
IB=I+I+2√I√I‌cos‌

π

2

=2I
Therefore intensities of radiation at A,B and C will be in the ratio
IA:IB:IC=4I:2I:0 =2:1:0