A screen is placed at `50cm` from a single slit, which is illuminated with `600nm` light. If separation between the first and third minima in the diffraction pattern is `3.0mm`, then width of the slit is:

Explanation

Position of first minima on a single slit diffraction pattern is given by
`d sin theta = n lambda `
For small value of `theta, sin theta = theta = y/D `
`:. Yd/D = n lambda or y = (n lambda D)/d`
`:.` Distance between third order minima and first order minima will be
`Deltay = y_3 -y_1 = ((3-1)(lambdaD))/d = (2lambdaD)/d `
Substituting the values, we have
` Deltay = ((2)(6xx 10^-7)(0.5))/(3 xx 10^(-3))`
`= 2 xx10^(-4) m`
= 0.2 mm