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JEE Main 20211 SeptemberEvening Shift
Exam
JEE Main
Year
2021
Date
1 September
Shift
Evening Shift
Subject
Physics
Chapter
Thermodynamics

JEE Main 2021 · 1 September · Evening Shift · Physics · Thermodynamics

The width of one of the two slits in a Young's double slit...

The width of one of the two slits in a Young's double slit experiment is three times the other slit. If the amplitude of the light coming from a slit is proportional to the slit-width, the ratio of minimum to maximum intensity in the interference pattern is x:4x: 4 where xx is _______ .

Correct answer

1

Step-by-step solution

Given amplitude ∝\propto slit widthAlso intensity ∝( Amplitude )2∝( Slit width )2I1I2=(31)2=9⇒I1=9I2Imin⁡Imax⁡=(I1−I2I1+I2)2=(3−13+1)2=14=x4⇒x=1\propto(\text{ Amplitude })^2 \propto(\text{ Slit width })^2 \frac{I_1}{I_2}=\left(\frac{3}{1}\right)^2=9 \Rightarrow I_1=9 I_2 \frac{I_{\min }}{I_{\max }}=\left(\frac{\sqrt{I_1}-\sqrt{I_2}}{\sqrt{I_1}+\sqrt{I_2}}\right)^2=\left(\frac{3-1}{3+1}\right)^2=\frac{1}{4}=\frac{x}{4} \Rightarrow x=1
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