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. `(b)/(d),(b)/(3d),(b)/(5d)`
B. `(b^(2))/(2d).(b^(2))/(4d),(b^(2)),(6d)`
C. `(b^(2))/(d).(b^(2))/(3d),(b^(2)),(5d)`
D. `(b)/(2d),(b)/(4d),(b)/(6d)`

Answer

C

Explanation

The situation is shown in the figure M

The path different between the waves reaching the point P is `trianglep=BP=AP`
The path difference between the waves reaching the point P is `triangleP=BP-AP`
`=((d^(2)+B^(2))1/2-d=d((1+(b^(2))/(d^(2))^(1)/(2)-d=d[(1+(1))/(2)(b^(2))/(d^(2))]-d=(b^(2))/(2d)`
For a dark band `triangleP=(b^(2))/(2d)=(2n-1)(lambda)/(2)`
Where,`n =1,2,3 or (lambda)=(1)(2n-1).(b^(2))/(d)`
Hence, the missing wavelengths are `(b^(2))/(d),(b^(2))/(3d),(b^(2))/(5d)`