Question

For three experiments, Fig.36-31 gives the parameter of Eq. 36-20 versus angle in two-slit interference using light of wavelength 500 nm. The slit separations in the three experiments differ. Rank the experiments according to (a) the slit separations and (b) the total number of two slit interference maxima in the pattern, greatest first.

Short answer

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

Step-by-step solution

The given data

Given for three experiments, the parameter$\beta$ of versus angle$\theta$ in two-slit interference using light of wavelength 500 nm.

The slit separations in the three experiments differ.

Concept and Formula used

In a double split experiment for diffraction,

$\beta =\frac{\pi d}{\lambda }\sin \theta$

$d$is slit separation , and$\lambda$ is wavelength.

(a) Rank according to slit separation

Now, from the equation

$\beta =\frac{\pi d}{\lambda }\sin \theta$

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

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

(b) Rank according to total diffraction maxima

Since the wavelengths are same, the smaller slit will produce more maxima.

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