Two coherent monochromatic light beams of intensities 4 and 9 are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is x. The value of x is ________. [2025]

Question

Two coherent monochromatic light beams of intensities 4 $I$ and 9 $I$ are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is x $I$ . The value of x is ________. [2025]

Smart Achievers · Accepted Answer

(24)

$I_{\max} = {(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2} = {(\sqrt{4 I} + \sqrt{9 I})}^{2} = 25 I$

$I_{\min} = {(\sqrt{I_{1}} - \sqrt{I_{2}})}^{2} = {(\sqrt{4 I} - \sqrt{9 I})}^{2} = I$

$I_{\max} - I_{\min} = 24 I \Rightarrow x = 24$

Solution

Q.
Two coherent monochromatic light beams of intensities 4 $I$ and 9 $I$ are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is x $I$ . The value of x is ________. [2025]

Ans.
(24)

$I_{\max} = {(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2} = {(\sqrt{4 I} + \sqrt{9 I})}^{2} = 25 I$

$I_{\min} = {(\sqrt{I_{1}} - \sqrt{I_{2}})}^{2} = {(\sqrt{4 I} - \sqrt{9 I})}^{2} = I$

$I_{\max} - I_{\min} = 24 I \Rightarrow x = 24$

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Solution

Q. Two coherent monochromatic light beams of intensities 4I and 9I are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is xI. The value of x is ________. [2025]

Ans. (24) Imax=(I1+I2)2=(4I+9I)2=25I Imin=(I1–I2)2=(4I–9I)2=I Imax–Imin=24I ⇒ x = 24

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Q.
Two coherent monochromatic light beams of intensities 4 $I$ and 9 $I$ are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is x $I$ . The value of x is ________. [2025]

Ans.
(24)

$I_{\max} = {(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2} = {(\sqrt{4 I} + \sqrt{9 I})}^{2} = 25 I$

$I_{\min} = {(\sqrt{I_{1}} - \sqrt{I_{2}})}^{2} = {(\sqrt{4 I} - \sqrt{9 I})}^{2} = I$

$I_{\max} - I_{\min} = 24 I \Rightarrow x = 24$