The interference pattern is obtained with two coherent light sources of intensity ratio $4: 1$. And the ratio $\frac{I_{\text {max }}+I_{\text {min }}}{I_{\text {max }}-I_{\text {min }}}$ is $\frac{5}{x}$. Then, the value of $x$ will be equal to:

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Wave Optics

The interference pattern is obtained with two coherent light sources of intensity ratio

4 : 1

. And the ratio

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

\frac{5}{x}

. Then, the value of

x

will be equal to:

(A)3
(B)4✓ Correct
(C)2
(D)1

Answer: (B)

Solution

For two coherent sources with intensity ratio

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

, we have

\frac{I _{max}}{I _{min}} = (\frac{I _{1} + I _{2}}{I _{1} - I _{2}})^{2} = (\frac{2 + 1}{2 - 1})^{2} = 9

. Using componendo-dividendo:

\frac{I _{max} + I _{min}}{I _{max} - I _{min}} = \frac{9 + 1}{9 - 1} = \frac{10}{8} = \frac{5}{4}

. Comparing with

\frac{5}{x}

, we get

x = 4

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Single correct option

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