Question

$\frac{5\lambda }{ka}$ is the angular divergence between the first minima and third maxima on either side of the central line. Then $k$ is

(Assume $\lambda <<a,a$ is slit width).

Answer 1

The angular position of $1^{st}$ minima is

$\sin {\theta }_1=\frac{\lambda }{a}$

${\theta }_1=\frac{\lambda }{a}(\because {\theta }_1\text{is small})$

The angular position of $3^{rd}$ maxima is

$\sin {\theta }_2=\frac{7\lambda }{2a}$

${\theta }_2=\frac{7\lambda }{2a}(\because {\theta }_2\text{is small})$

The angular divergence between $1^{st}$ minima and $3^{st}$ maxima is

$\theta ={\theta }_2-{\theta }_1$

$\therefore \theta =\frac{5}{2}\frac{\lambda }{a}$

Correct answer : $2$