Obtain the formulas angular width and linear width of central maximum.

Explanation

Width of central maximum is the distance between the first minimum on either side of the central maximum.
Suppose, width of slit a is very small (in the order of mm) and the distance between slit and screen is D (in the order of meter). This is shown in figure.

For a minimum of one side of the central maximum on the screen `theta=(lamda)/(a)`
where `theta` is half the width of angular width of central maximum.
`:.` Angular width of central maximum `2theta=(2lamda)/(a)`
`2theta=(arc(beta_(0)))/("radius"(D))`
`:.beta_(0)=Dxx2theta`
`=(2Dlamda)/(a)" "....(1)" "[:.theta=(lamda)/(a)]`
Angle of `(n+1)^(th)` order minimum `beta_(0)` is width of linear central maximum. It is minimum distance between the central maximum distance.
Linear width of secondary maximum : The angular width in .n. means the least angular difference in n and (n + 1).
`:.` The angle of least angular in .n., `theta_(n)=(nlamda)/(a)` Angle of `(n+1)^(th)` order minimum
`theta_(n+1)=((n+1)lamda)/(Q)`
`:.` Angular width of `n^(th)` secondary maximum, `theta_(n+1)-theta_(n)=(n+1)(lamda)/(a)-(nlamda)/(a)`
`=(lamda)/(a)`
`:.` The linear widht of `n^(th)` secondary maximum =angular width `xx` D
`beta=(lamda)/(a)xxD" "......(2)`
`:.(beta_(0))/(beta)=2" "` [ `:.` Ratio of equation (1) and (2)]
`:.beta_(0)=2beta`