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(gtgtb)` 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 wavelength are

Options

A. (i), (ii)
B. (ii), (iii)
C. (i), (iii)
D. (ii), (iv)

Answer

C

Explanation

`Deltax=S_(2)P-S_(1)P=sqrt(b^(2)+d^(2))-d`
`=d(1+b^(2)/d^(2))^(1/2)-d`
`=d(1+b^(2)/(2d^(2)))-d=b^(2)/(2d)`
For missing wavelengths (use condition of minima)
`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)`