In a Fraunhofer diffraction at single slit of width d with incident light of wavelength 5500 Ã…, the first minimum is observed, at angle `30^(@)`. The first secondary maximum is observed at an angle `theta=`

Options

A. `"sin"^(-1)((1)/(sqrt(2)))`
B. `"sin"^(-1)((1)/(4))`
C. `"sin"^(-1)((3)/(4))`
D. `"sin"^(-1)((sqrt(3))/(2))`

Answer

C

Explanation

Slit width = d
`lambda=5500 Ã…=5.5xx10^(-7)m, theta_(n)=30^(@)`
For first secondary minima, `d "sin"theta_(n)=lambda`
`d=(lambda)/("sin"theta_(n))=(5.5xx10^(-7))/("sin"30^(@))=11xx10^(-7)m`
For first secondary maxima, `d "sin"theta_(n)=(3lambda)/(2)`
i.e. `"sin" theta_(n)=(3lambda)/(2d)=(3xx5.5xx10^(-7))/(2xx11xx10^(-7))`
` "sin"theta_(n)=(3)/(4)" or "theta_(n)="sin"^(-1)(3//4)`