Question

Plane microwaves are incident on a long slit having a width of $5.0\text{cm}$. Calculate the wavelength of the microwaves if the first diffraction minimum is formed at $\theta ={30}^{\circ }$.

• A. $2\text{cm}$
• B. $2.5\text{cm}$
• C. $5\text{cm}$
• D. $4\text{cm}$

Answer 1

The correct option is B $2.5\text{cm}$

Given:
$b=5\text{cm};\theta ={30}^{\circ }$

The condition for formation of $n^{th}$ minimum in diffraction pattern is given by,

$b\sin \theta =n\lambda$

$\Rightarrow \lambda =\frac{b\sin \theta }{n}$

Here, $n=1$

$\Rightarrow \lambda =\frac{5\text{cm}\times \sin {30}^{\circ }}{1}=2.5\text{cm}$

Hence, option $\left(\text{B}\right)$ is correct.

Why this Question? Concept :- For the formation of dark fringe in a single slit diffraction : $b\sin \theta =n\lambda$