Question

In a single slit diffraction experiment, light of wavelength $\lambda$ passes through a slit of width $a$ and produces a diffraction pattern with $I_0$ as the intensity of the central maximum.
Find the ratio of intensity at a point midway between second and third minima to the intensity at the central maxima.

• A. $\frac{1}{22}$
• B. $\frac{7}{55}$
• C. $\frac{49}{3025}$
• D. $\frac{1}{5}$

Answer 1

The correct option is C $\frac{49}{3025}$

Intensity at a point is given by

$I=I_0\frac{{\sin }^2\beta }{{\beta }^2}$

Where, $\beta =\frac{\pi a\sin \theta }{\lambda }$

$I_0\to$ Intensity at central maximum.

$\Rightarrow$ The point midway between second minima and third minima will be second maximum.

$\Rightarrow \sin \theta =\frac{5\lambda }{2a}\text{[For second maxima]}$

$\Rightarrow \beta =\frac{5\pi }{2}$

$\Rightarrow I=I_0{\left(\frac{\sin \left(5\pi /2\right)}{5\pi /2}\right)}^2$

$\Rightarrow I=I_0{\left(\frac{2\times 7}{5\times 22}\right)}^2\Rightarrow \frac{I}{I_0}=\frac{49}{3025}$

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