Question

In Young’s double slit experiment, the slits are separated by 0.5 mm and screen is placed 1.0 m away  from the slit. It is found that the 5^th bright fringe is at a distance of 4.13 mm from the 2^nd dark fringe.  Find the wavelength of light used.  

Answer 1

Given d =  0.5mm
D = 1.0m 

5^th bright `x_n = ( n lambda D ) / d`

`x_5 = 5 ( lambda D) /d`

2^nd dark `x_m = (2m-1) (lambdaD)/(2d)`

`5(lambdaD)/(d) = (3 lambdaD)/(2d) = 4.13 xx 10^(-3) ⇒ ( 7lambdaD)/(2d) = 4.13  xx 10^(-3)`

`(7lambda xx 1)/(2 xx5 xx10^(-4)) = 4.13 xx 10^(-3)    lambda = (2 xx 4.13 xx 10^(-3) xx 5 xx 10^(-4))/7`

`lambda = 5.9 xx 10^(-7) m`