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. `lamda=(b^(2))/(2d)`
B. `lamda=(b^(2))/(3d)`
C. `lamda=(b^(2))/(4d)`
D. `lamda=(2b^(2))/(3d)`

Answer

B

Explanation

The point P is directly in front of `s_(1)` and it is a distance `b/2` from O.
The path difference`=s_(2)P-s_(1)P=(b^(2))/(2d)`
Those wavelengths will be missing for which
`Deltax=(lamda_(1))/(2),(3lamda_(2))/(2),(5lamda_(2))/(2)`, . .
`therefore lamda_(1)=2Deltax=2((b^(2))/(2d))=(b^(2))/(d)`
and `lamda_(2)=(2Deltax)/(3)=(b^(2))/(3d)` (missing wavelength)
`sinlamda_(3)=(2Deltax)/(5)=(b^(2))/(5d)`
Thus the missing wavelength is `lamda_(2)=(b^(2))/(3d)`