Question

For three experiments, Fig. 36-31 gives $\mathit{\alpha }$versus angle $\mathit{\theta }$ in one-slit diffraction using light of wavelength 500 nm. Rank the experiments according to (a) the slit widths and (b) the total number of diffraction minima in the pattern, greatest first.

Short answer

1. The rank will be A, B and C
2. The rank will be A, B and C.

Step-by-step solution

The given data

Given a figure depicting $\alpha$versus angle $\theta$in one-slit diffraction using light of wavelength 500 nm.

Concept and Formula used

In a double split experiment for diffraction,

$\alpha =\frac{\pi a}{\lambda }\sin \theta$

a is distance between slit , and$\lambda$ is wavelength.

(a) Rank according to slit width

Now, from the equation

$\alpha =\frac{\pi a}{\lambda }\sin \theta$

It is clear that graph will be greater for larger values of a.

So, rank according to slit width (greatest first) is A, B and C.

(b) Rank according to total diffraction minima

Since the wavelengths are same, the larger slit will produce more minima.

So, the rank will be A, B and C.