Two spectral lines of sodium `D_(1) and D_(2)` have wavelengths of approximetely plane wave on to a slit of width `2 micrometer`. A screen is located `2m` from the slit. Find the spacing between the first maxima of two sodium lines as measured on the screen.

Explanation

Here,
`lambda_(1) = 5890 Å = 5890 xx 10^(-10)m`,
`a = 2 mu m = 2 xx 10^(-6)m`
`lambda_(2) = 5896 Å = 5896 xx 10^(-10)m, D = 2 m`
For the first secondary maxima,
`sin theta = (3 lambda_(1))/(2 a) = (x_(1))/(D)`
or `x_(1) = (3 lambda_(1) D)/(2 a) and x_(2) = (3 lambda_(2) D)/(2 a)`
`:.` Spacing between the first secondary maxima of two sodium lines
`= x_(2) - x_(1) = (3 D)/(2 a)(lambda_(2) - lambda_(1))`
`= (3 xx 2(5896 - 5890) xx 10^(-10))/(2 xx 2 xx 10^(-6)) = 9 xx 10^(-4)m`