In young double slit experiment, slit with ratio is 3:2 then find out the ratio of the maximum and minimum intensity of interference of light.

Asked by sparbin0019 | 25th Jan, 2019, 09:21: AM

Expert Answer:

Width is directly proportionl to intensity 
Intensity is directly proportional to the square of amplitude
 
w subscript 1 over w subscript 2 equals I subscript 1 over I subscript 2 equals fraction numerator A subscript 1 superscript 2 over denominator A subscript 2 superscript 2 end fraction space equals 3 over 2 A subscript 1 over A subscript 2 equals square root of 3 over 2 end root A subscript 1 equals space square root of fraction numerator begin display style 3 end style over denominator 2 end fraction end root A subscript 2 space space space.... left parenthesis 1 right parenthesis space M a x i m u m space i n t e n s i t y space i s space t h e space s q u a r e space o f space s u m space o f space b o t h space a m p l i t u d e s M i n i m u m space i n t e n s i t y space i s space t h e space s q u a r e space o f space d i f f e r e n c e space o f space b o t h space a m p l i t u d e s space fraction numerator I subscript m a x end subscript over denominator I space m i n end fraction equals fraction numerator left parenthesis A subscript 1 plus A subscript 2 right parenthesis squared over denominator left parenthesis A subscript 1 minus A subscript 2 right parenthesis squared end fraction equals space fraction numerator begin display style open parentheses square root of 3 over 2 end root A subscript 2 space plus A subscript 2 close parentheses squared end style over denominator open parentheses square root of 3 over 2 end root A subscript 2 space minus space A subscript 2 close parentheses squared end fraction space equals fraction numerator begin display style open square brackets open parentheses square root of 3 plus square root of 2 close parentheses A subscript 2 close square brackets squared end style over denominator open square brackets open parentheses square root of 3 minus square root of 2 close parentheses A subscript 2 close square brackets squared end fraction equals fraction numerator begin display style open parentheses square root of 3 plus square root of 2 close parentheses squared end style over denominator begin display style open parentheses square root of 3 minus square root of 2 close parentheses squared end style end fraction.... left parenthesis f r o m space left parenthesis 1 right parenthesis right parenthesis equals fraction numerator 5 plus 2 square root of 2 square root of 3 over denominator 5 minus 2 square root of 2 square root of 3 end fraction equals fraction numerator left parenthesis 5 plus 2 square root of 6 right parenthesis over denominator left parenthesis 5 minus 2 square root of 6 right parenthesis end fraction equals fraction numerator begin display style left parenthesis 5 plus 2 square root of 6 right parenthesis end style over denominator begin display style left parenthesis 5 minus 2 square root of 6 right parenthesis end style end fraction cross times fraction numerator left parenthesis 5 minus 2 square root of 6 right parenthesis over denominator left parenthesis 5 minus 2 square root of 6 right parenthesis end fraction O n space r a t i o n a l i z a t i o n space w e space g e t comma space equals fraction numerator 25 minus 24 over denominator 49 minus 20 square root of 6 end fraction almost equal to fraction numerator 1 over denominator 0.02 end fraction almost equal to space fraction numerator 1 over denominator begin display style 2 over 100 end style end fraction equals 100 over 2 equals 50 over 1
Thus. Imax : Imin = 50:1

Answered by Shiwani Sawant | 25th Jan, 2019, 02:32: PM

Related Videos

This video explains Young's double slit experiment for interference.

This video establishes few mathematical expressions pertaining to interfere...

This video provides expert tips and contains practice problems on interfere...

All Questions Ask Doubt