A single narrow slit of width a is illuminated by monochromatic parallel ray of light of wavelength 700 nm. Find the value of a in each case following the given conditions-
(i) first minimum for `30^(@)` diffraction angle and
(ii) first secondary maximum for `30^(@)` diffraction angle.

Explanation

From the conditions of formation of n th minimum,
a `sintheta = nlambda`
or, `a"" sin 30^(@) = 1 xx 700 xx 10^(-9) [ because theta = 30^(@) , n = 1 `
and `lambda = 700" nm" = 700xx 10^(-9)`m]
`therefore` a`= (700xx10^(-9))/( (1)/(2)) = 14 xx 10^(-7) ` m
(ii) From the condition of formation of n th secondary maximum,
` a sin theta = (2n + 1)(lambda)/(2)`
or , a `sin 30^(@) = (3)/(2) xx 700 xx 10^(-9) `
[`because = 30^(@)`, for 1st secondary maximum , n = 1
and `lambda = 700 "mm" = 700xx 10^(-9) `m ]
`therefore " " a = 21 xx 10^(-7) `m