A Young's doublc-slit experiment is performed using monochromatic light of wavelength λ. The intensity of light at a point on the screen, where the path difference is λ, is K units. The intensity of light at a point where the path difference is A λ/6 is given by n K/12, where n is an integer. The value of n is......

JEE Mains · Physics · STD 12 - Wave optics

A Young's doublc\(-\)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 A \(\frac{\lambda}{6}\) is given by \(\frac{n K}{12},\) where \(n\) is an integer. The value of \(n\) is\(......\)

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Verified Solution

Correct Answer

(A) \(9\)

Detailed explanation

\(I _{\max }= k\)

\(I _{1}= I _{2}= K / 4\)

\(\Delta x =\lambda / 6 \Rightarrow \Delta \phi=\pi / 3\)

\(I = I _{1}+ I _{2}+2 \sqrt{ I _{1} I _{2}} \cos \phi\)

\(I =\frac{ K }{4}+\frac{ K }{4}+2 \times \frac{ K }{4} \frac{1}{2}\)

\(=\frac{ K }{2}+\frac{ K }{4}=\frac{3 K }{4}=\frac{9 K }{12}\)

\(n =9\)

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