In a diffraction pattern due to a single slit of width a, the first minimum is observed at an angle `30^(@)` when light of wavelength 5000 Å is incident on the slit. The first secondary minimum is observed at an angle of

Options

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

Answer

B

Explanation

For first minimum, the path difference between extreme waves, `asintheta=lambda`
Here `theta=30^(@)impliessintheta=(1)/(2)`
`:.a=2lambda` …(i)
For first secondary maximum, the path difference between extreme waves
`asintheta=(3)/(2)lambda "or" (2lambda)sintheta.=(3)/(2)lambda` [Using eqn (i)]
or `sintheta.=(3)/(4):.theta.=sin^(-1)((3)/(4))`