Lights of wavelengths `lambda_(1)=4500 Å, lambda_(2)=6000 Å` are sent through a double slit arrangement simultaneously. Then

Options

A. no interference pattern will be formed
B. the thrid bright fringe of `lambda_(1)` will coincide with the fourth bright fringe of `lambda_(2)`
C. the thrid bright fringe of `lambda_(2)` will coincide with the fourth bright fringe of `lambda_(1)`
D. the fringes of wavelenths `lambda_(1)` will bw wider than the fringes of wavelenghts `lambda_(2)`

Answer

C

Explanation

`x_(n)=(D)/(d)n_(1) lambda_(1)=(D)/(d) n_(2) lambda_(2)`
`:. (n_(1))/(n_(2))=(lambda_(2))/(lambda_(1))`
`:. n_(1)=(lambda_(2))/(lambda_(1)) n_(2)=(6000)/(45000)n_(2)=(4)/(3) n_(2)`
`:. 3n_(1)=4n_(2)`
Thus `3^(rd)` bright ringe of `lambda_(2)` will coinide with `4^(th)` bright fringe of `lambda_(1)`