White light is used to illuminate the two slits in a Young's double slit experiment. The separation between the slits is b and the 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)//d`
B. `lamda=2b^(2)//d`
C. `lamda=b^(2)//3d`
D. `lamda=2b^(2)//3d`

Answer

AC

Explanation

Separation between slits=b, screen distance d
`(gt gt b)`
Path difference at `O` must be odd multiple of `(lamda)/(2)`
for missing wavelength `S_(2)O-S_(1)O=(nlamda)/(2)`
`impliessqrt(d^(2)+b^(2))-d=(nlamda)/(2)`
`impliesd^(2)+b^(2)=d^(2)+(n^(2)lamda^(2))/(4)+2xx(nlamda)/(2)xxd`
`implieslamda=(b^(2))/(nd)(n=1,3,5)`