98. Figure here shows P and Q as two equally intense
coherent sources emitting radiations of wavelength
20 m. The separation PQ is 5 m and phase of P is
ahead of the phase of Q by 90°. A, B and Care
three distant points of observation equidistant from the
mid-point of PQ. The intensity of radiations at A, B,
C will bear the ratio
Answers
Given:
Figure shows P and Q as two equally intense coherent sources emitting radiations of wavelength 20 m.
The separation PQ is 5 m and phase of P is ahead of the phase of Q by 90°.
To find:
The intensity of radiations at A, B, C will bear the ratio
Solution:
From given, we have,
P and Q as two equally intense coherent sources emitting radiations of wavelength 20 m.
The separation PQ is 5 m.
⇒ At A,
PA - QA = PQ = 5 m
= λ/4 = 20/4 = Δx
we have,
ΔΦ' = 2π/λ Δx
= 2π/λ × λ/4
= π/2
As the phase of P is ahead of the phase of Q by 90°.
Net phase difference Ф = π/2 - π/2 = 0
A, B and Care three distant points of observation equidistant from the mid-point of PQ.
At A, I_A = 4I'
At B, Ф = π/2, I_B = 2I'
At C, Δx = QA - PA = λ/4 Φ' = π/2
Now consider, the net phase difference,
Ф = π/2 + π/2 = π
I_C = 0
I_A : I_B : I_C = 4I' : 2I' : 0
∴ I_A : I_B : I_C = 2I' : I' : 0
Option (d) is correct.