A Young's double-slit experiment is performed using monochromatic light of wavelength $\lambda$. The intensity of light at a point on the screen, where the path difference is $\lambda$, is K units. The intensity of light at a point where the path difference is ${\lambda \over 6}$ is given by ${{nK} \over {12}}$, where n is an integer. The value of n is __________.
Answer (integer)
9
Solution
From 1<sup>st</sup> case,
<br><br>$\Delta$$\phi$ = ${{2\pi } \over \lambda } \times \lambda$ = 2$\pi$
<br><br>$\therefore$ I<sub>net</sub> = 4Icos<sup>2</sup> ${{\Delta \phi } \over 2}$ = 4I = K (Given)
<br><br>From 2<sup>nd</sup> case,
<br><br>$\Delta$$\phi$ = ${{2\pi } \over \lambda } \times {\lambda \over 6}$ = ${\pi \over 3}$
<br><br>$\therefore$ I<sub>net</sub> = 4I cos<sup>2</sup> ${{\Delta \phi } \over 2}$
<br><br>= 4I $\times$ ${3 \over 4}$ = ${3 \over 4}K$
<br><br>$\therefore$ According to question,
<br><br>${{nK} \over {12}}$ = ${3 \over 4}K$
<br><br>$\Rightarrow$ n = 9
About this question
Subject: Physics · Chapter: Optics · Topic: Reflection and Mirrors
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