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`(gtb) from the slits. At a point on the screen directly in front of one of the slits, certain wavelength are missing. Some of these missing wavelength are

Explanation

At `P`, path difference
`Deltax=S_(2)P-S_(1)P=(D^(2)+b^(2))^(1//2)-D`
`=D(1+b^(2)/D^(2))^(1/2)-D`
`=D(1+b^(2)/(2D^(2)))^(1/2)-D=b^(2)/(2D)`
For missing wavelengths
`Deltax=(2n+1)lambda/2`
`b^(2)/(2D)=(2n+1)lambda/2`
`lambda=b^(2)/((2n+1)D)`
`n=0, lambda=b^(2)/D`
`n=1, lambda=b^(2)/(3D)`
`n=2, lambda=b^(2)/(5D)`
Missing wavelength: `b^(2)/D,b^(2)/(3D),b^(2)/(5D), ...`