A beam of light of two wavelengths `6500Å` and `5200Å`, is used to obtain interference fringes in Young's double slit experiment. Suppose the `m^(th)` brght fringe due to `6500Å` coincides with `n^(th)` bright fringe due to `5200Å` at a minimum distance from the cental maximum. Then

Options

A. m = 10, n = 8
B. m = 8, n = 10
C. m = 5, n = 4
D. m = 4, n = 5

Answer

B

Explanation

Position of `m^(th)` bright fringe `= (mD lamda)/(d) = y_(w) " here" lamda= 6500Å`
Position of `n^(th)` bright fringe due to `lamda = 5200 Å`
`y_(n) = (nD lamda_(1))/(d) " as " y_(m)= y_(n)`
`:. m xx 6500 = n xx 5200`
`(m)/(n) = (4)/(5)`. As both have to be even.
`:. m= 8,n=10`