Question

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
​

Answer 1

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.