A slit of width is illuminated by white light. For red light `(lambda=6500Å)`, the first minima is obtained at `theta=30^@`. Then the value of will be

Options

A. `3250Å`
B. `6.5 xx 10^(-4)cm`
C. `1.3` micron
D. `2.6 xx 10^(-4)cm`

Answer

C

Explanation

`sin theta = (n lambda)/(a)`, for `n =1, sin theta = (lambda)/(a)`
`:. a = (lambda)/(sin theta) = (6500 xx 10^(-10))/(sin 30^(@))`
`a = 13000 xx 10^(-10)m`
`a = 1.3 xx 10^(-6)m`
`a = 1.3` micron