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