Light of wavelength `5000 Å` is incident normally on a slit of width `2.5 xx 10 ^(-4)` cm. The angular position of second minimum from the central maximum is

Options

A. `sin ^(-1) ((1)/(5))`
B. `sin ^(-1) ((2)/(5))`
C. `((pi)/(3))`
D. `((pi)/(6))`

Answer

B

Explanation

We know that,
Angular width of central maximum `= (2 lamda )/(a)`
where ,` lamda =` wavelength of light,
`a = ` width of single slit,
So,` sin theta = ( 2 lamda )/(a)`
where `lamda = 5000 Å = 5000 xx 10 ^(-10) m`
`a = 2.5 xx 10 ^(-8) m`
`implies sin theta = (2 xx 5000 xx 10 ^(-10))/( 2.5 xx 10 ^(-6))`
`sin theta = ( 10000- xx 10 ^(-10))/( 25 xx 10 ^(-6))`
`sin theta = (10 xx 10 ^(10) xx 10 ^(-10))/(25)`
`sin theta = (10)/(25)`
`theta = sin ^(-1) ((2)/(5))`