Two coherent light waves of intensity 5 \times 10^{-2} {\Wm}^{-2} each superimpose and produce the interference pattern on a screen. At a point where the path difference between the waves is \frac{\lambda}{6}, \lambda being wavelength of the wave, find the (a) phase difference between the waves (b) resultant intensity at the point (c) resultant intensity in terms of the intensity at the maximum

CBSE Class 12 Physics 2020 Outside Delhi Set 1 Paper

Question : 33 of 37

Marks: +1, -0

Two coherent light waves of intensity

5 ×

10^{-2} {\Wm}^{-2}

each superimpose and produce the interference pattern on a screen. At a point where the path difference between the waves is

\;{λ}/{6}, λ

being wavelength of the wave, find the
(a) phase difference between the waves
(b) resultant intensity at the point
(c) resultant intensity in terms of the intensity at the maximum

Solution:

(a)

∆ x=\;{λ ∆ϕ}/{2 π}

, where

∆ x=

Path difference and

\;∆ ϕ=\;\text " Phase difference "\;

\;∆ x=\;{λ}/{6}

\; ∴ ∆ ϕ=\;\text " phase difference "\;

=\;{λ}/{6} × \;{2 π}/{λ}=\;{2 π}/{6}

(b) Resultant intensity

= {\I}= {\I}_0 \cos ^2 \;{∆ ϕ}/{2}

\;\text " Or, "\;\;I=I_0 \cos ^2 \;{π}/{6}

\;\text " Or, "\;\;I=5 × 10^{-2} \cos ^2 \;{π}/{6}

\;\text " Or, "\;\;I=5 × 10^{-2} (\;{{√{3}}}/{2}) ^2

∴ \;I=3.75 × 10^{-2} {\Wm}^{-2}

= {\I}_{\max }=4 {\I}_0

Resultant intensity

= {\I}_{\;\text "RESULTANT "\;}=\;{3 {\l}_0}/{4}

= {\I}_{\max }=4 {\I}_0

\;\text " Resultant intensity "\;= {\I}_{\;\text "RESULTANT "\;}=\;{3 {\I}_0}/{4}

\;{ {\I}_{\;\text "RESULTANT "\;}}/{ {\I}_{\;\text "MAX "\;}}=\;{3 {\I}_0 \/ 4}/{4 {\I}_0}=\;{3}/{16}

∴ {\I}_{\;\text "RESULTANT "\;}=\;{3}/{16} {\I}_{\;\text "MAX "\;}

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