The ratio of intensities of consecutive maxima in the diffraction pattern due to a single slit is

Options

A. 1: 4: 9
B. 1 : 2 : 3
C. `1: (4)/(9pi^(2)):(4)/(25pi^(2))`
D. `1: (1)/(pi^(2)):(1)/(pi^(2))`

Answer

C

Explanation

Intensity `I= I_(0)[(sinalpha)/(alpha)]^(2) alpha= (phi)/(2)`
For nth secondary maxima
`dsintheta= ((2n+1)/(2))lambda`
`alpha= (phi)/(2)= (pi)/(lambda)(dsintheta)= ((2n+1)/(2))pi`
`:. I= I_(0)[(sin((2n+1)/(2))pi)/(((2n+1)/(2))pi)]= (I_(0))/(((2n+1)/(2)pi)^(2))`
`I_(0): I_(1):I_(2)= I_(0):(4)/(9pi^(2))I_(0): (4)/(25pi^(2))I_(0)= 1: (4)/(9pi^(2)): (4)/(25pi^(2))`