A beam of light consisting of two wavelength `6500Å&5200Å`is used to obtain interferance fringes in a young's double slit experiment .The distance between the slits is `2.0mm` and the distance between the plane of the slits and thescreen is `120cm`,.what is the least distance from the central maximum where the bright fringes due to both the wave length coincides?

Options

A. 0.156 cm
B. 0.152 cm
C. 0.17
D. 0.16 cm

Answer

A

Explanation

Suppose the `m^(th)` bright fringe of 6500Å coincides with the `n^(th)` bright fringe of 5200Å
`X_(n)=(mlamda_(1)D)/d=(nlamda_(2)D)/d`
`rArr(mxx6500xxD)/d=(nxx5200xxD)/drArrm/n=5200/6500=4/5`
`therefore` distance y is
`y=(mlamda_(1)D)/d=(4xx6500xx10^(10)xx1.2)/(2xx10^(-3))rArry=0.156cm`.