In a double slit experiment, the distance between the slits is 5.0 mm and the slits are 1.0m from the screen. Two interference patterns can be seen on the screen one due to light with wavelength 480nm, and the other due to light with wavelength 600nm. What is the separation on the screen between the third order bright fringes of the two intergerence patterns?

Options

A. 0.20 mm
B. 0.05 mm
C. 0.072 mm
D. 0.09 mm

Answer

C

Explanation

The position of `n^(th)` order bright fringe from the central bright fringe is
`x_(n)=(nlamdaD)/(d)`
where, `lamda=`Wavelength of light used
`D=`Distance of screen from the slits
d=Distance between the slits
For wavelength `lamda(=480nm)`, the position of `3^(rd)` order bright fringe from the central bright fringe is `x_(3)=(3lamdaD)/(d)`
For wavelength `lamda.(=600nm)`, the position of 3rd order bright fringe from the central bright fringe is `x_(3).=(3lamda.D)/(d)`
`therefore`The separation between the third order bright fringes of the two interference patterns is
`x_(3).-x_(3)=(3(lamda.-lamda)D)/(d)`
Here, `lamda=480xx10^(-9)m,lamda.=600nm=600xx10^(-9)m`
`D=1.0m,d=5.0mm=5.0xx10^(-3)mm`
`therefore x_(3).-x_(3)=(3(600-480)xx10^(-9)mxx1.0)/(5.0xx10^(-3))`
`=0.072xx10^(-3)m=0.072mm`.