Question

In a single slit diffraction pattern, the distance between the first maximum on the left and the first maximum on the right is $$5mm$$. The screen on which the diffraction pattern is displaced is at a distance of $$80cm$$from the slit. The wavelength is $6000angstrom$. The slit width is mm is about
A) $$0.576$$
B) $$0.348$$
C) $$0.192$$
D) $$0.096$$

Answer 1

Hint: Diffraction: It is the phenomenon of bending of light around the corners of small obstacles or apertures and the consequent spreading into the regions of geometrical shadows.

Formula used:
$\text{d = }{\displaystyle \frac{\text{m}\lambda \text{D}}{\text{y}}}$, here, d=slit width, $\lambda =$wavelength of the light wave, $D$=distance of the screen from the slit, y=distance between the first maxima from the center, $m$= order of the fringes.

Complete step-by-step solution:
Given details: The order of the fringes, $m=1$,
Distance between the first maximum (or minimum) and central fringe is, $$y={\displaystyle \frac{5}{2}}=2.5cm$$,
Distance between the screen and the slit, $$D=80cm=800mm,$$
Wavelength if the light wave,$\lambda =6000angstorm$
 Single slit diffraction pattern:

Single slit diffraction can be performed through a single slit whose width is on the order of the wavelength of light, then the light wave is diffracted on the edge of the aperture forming a single slit diffraction pattern on the screen that is placed at a certain distance from the apparatus. Therefore, we can find the value of slit width using the above formula,
$\text{d = }{\displaystyle \frac{\text{m}\lambda \text{D}}{\text{y}}}$,
Substitution of the values in the given equations give,
$\Rightarrow \text{d = }{\displaystyle \frac{(1)(800)(6000)}{2.5}}$
Simplifying the given equations we get,
$\Rightarrow (1.92\text{x1}{\text{0}}^5){10}^{-7}$
=$\therefore 0.192mm$

Hence, The correct option is (C).

Note: There are two types of a single slit diffraction pattern,
Fresnel’s diffraction pattern: In this diffraction pattern, the screen and the slit are placed close to the aperture or the obstacles and the light after diffraction appears converging towards the screen.
Fraunhofer’s diffraction pattern: In this diffraction pattern, the source and the screen are placed at a large distance from the aperture or the obstacles.