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

Options

A. `lambda=(b^(2))/(d)`
B. `lambda=(b^(2))/(3d)`
C. `lambda=(2b^(2))/(d)`
D. both 'a' and 'b'

Answer

D

Explanation

Position of `n^(th)` minima is,
`x_(n)=(D)/(d)(2n-1) (lambda)/(2) :. lambda=(2*x_(x)*d)/(D(2n-1))`
Now, `x_(n)=b//2/ d =b and D=d`
`:.lambda=(2*(b//2)*b)/(d(2n-1))=(b^(2))/((2n-1)d)`
`:. lambda=(b^(2))/(d),(b^(2))/(3d),...... ( :. n=1,2,....)`
thus, correct option is d