CBSE Class 12-science Answered

Physic

Asked by balwansungh111334 | 13 Jul, 2022, 07:34: AM

Expert Answer

Resultant intensity I_R of two waves of radiation of intensities I₁ and I₂ is given as

begin mathsize 14px style I subscript R space equals space I subscript P space plus space I subscript Q space plus space 2 space square root of I subscript P end root space square root of I subscript Q end root space cos ϕ end style

.............................(1)

where

begin mathsize 14px style I subscript P end style

is intensity of radiation of source P ,

begin mathsize 14px style I subscript Q end style

is intensity of radiation of source Q and

begin mathsize 14px style ϕ end style

is phase difference between sources

At point A , radiation from source P has path difference 5m compare to radiation from source Q.

Phase difference for 5 m path difference = (5/20)2π = π/2

Since radiation from source P is ahead of source Q by phase (π/2) , additional phase lag (π/2) of source P due to path difference

makes the two sources in phase at point A.

Hence if we substitute

begin mathsize 14px style ϕ end style

= 0 in eqn.(1), we get

begin mathsize 14px style I subscript A space equals open parentheses square root of I subscript P end root space plus space square root of I subscript Q end root close parentheses squared space space space space end style

.................................(2)

At point B , there is no path difference for radiations from source P and source Q.

But initially source P is ahead of source Q by phase (π/2)

Hence if we substitute

begin mathsize 14px style ϕ end style

= (π/2) in eqn.(1), we get

begin mathsize 14px style I subscript B space equals space I subscript P space plus space I subscript Q space end style

.........................................(3)

At point C , radiation from source P leads a path difference 5m, hence leads additional phase difference (π/2).

Since initially source P is ahead of source Q by phase (π/2), total phase difference becomes π .

Hence if we substitute

begin mathsize 14px style ϕ end style

= π in eqn.(1), we get

begin mathsize 14px style I subscript C space equals open parentheses square root of I subscript P end root space minus space square root of I subscript Q end root close parentheses squared space space space space end style

............................(4)

If two sources have same intensity , then

begin mathsize 14px style I subscript A space equals space I subscript B space equals space I end style

Hence using eqn.(2) , eqn.(3) and eqn.(4) , we get the ratio of intensities as

begin mathsize 14px style I subscript A space colon space I subscript B space colon space I subscript C space equals space left parenthesis 2 square root of I space right parenthesis squared space colon space 2 I space colon space 0 space space equals space 2 space colon space 1 space colon space 0 end style

Answered by Thiyagarajan K | 13 Jul, 2022, 09:21: AM

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