White light is used to illuminate the two slits in Young's double slit experiment. The separation between the slits is b and the screen is at a distance `Dgt gt b` from slits. At a point on the screen directly in front of one of the slits, the missing wavelengths are

Options

A. A, B and C are correct
B. A and B are correct
C. B and D are correct
D. A and C are correct

Answer

D

Explanation

Path difference between the rays reaching in front of slit `S_(1) ` is
`S_(1) P - s_(2) P = (b^(2) + d^(2))^(1//2) - d`
For destructive interference at P
`S_(1)P - S_(2) P = ((2n -1))/(2) lambda`
`(b^(2) + d^(2)) ^(1//2) - d = ((2 n - 1))/(2) lambda`
`d (1 + (b^(2))/(d^(2)))^(1//2) -d = ((2n - 1))/(2) lambda`
`d (1 + (b^(2))/(2d^(2))+. . . . ) - d = ((2n - 1))/(2) lambda`
`(b^(2))/(2d) = ((2n -1))/(2) lambda`
`lambda = (b^(2))/((2n -1)d)`
Forn = 1,2,3. . . .
`lambda = (b^(2))/(d),(b^(2))/(3d)`