Two coherent sources of light interfere. The intensity ratio of two sources is $1: 4$. For this interference pattern if the value of $\frac{I_{\text{max}}+I_{\text{min}}}{I_{\text{max}}-I_{\text{min}}}$ is equal to $\frac{2\alpha+1}{\beta+3}$, then $\frac{\alpha}{\beta}$ will be:

JEE Main · 2022 · 27 Jul 2022 · Shift 2 · Wave Optics

Two coherent sources of light interfere. The intensity ratio of two sources is

1 : 4

. For this interference pattern if the value of

\frac{I _{max} + I _{min}}{I _{max} - I _{min}}

is equal to

\frac{2 α + 1}{β + 3}

, then

\frac{α}{β}

will be:

(A)1.5
(B)2✓ Correct
(C)0.5
(D)1

Answer: (B)

Solution

Given

\frac{I _{1}}{I _{2}} = \frac{1}{4}

, so

I_{2} = 4 I_{1}

. The maximum and minimum intensities are

I_{max} = I_{1} + I_{2} + 2 I_{1} I_{2} = I_{1} + 4 I_{1} + 2 4 I_{1}^{2} = 9 I_{1}

and

I_{min} = I_{1} + 4 I_{1} - 4 I_{1} = I_{1}

. Thus

\frac{I _{max} + I _{min}}{I _{max} - I _{min}} = \frac{10 I _{1}}{8 I _{1}} = \frac{5}{4}

. Comparing with

\frac{2 α + 1}{β + 3} = \frac{5}{4}

, we get

8 α + 4 = 5 β + 15

, giving

α = 2

and

β = 1

. Therefore

\frac{α}{β} = 2

JEE Main · 2022 · 27 Jul 2022 · Shift 2 · Single correct option

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