Question

An application of this principle is that a line mounted on transparent slide casts the same diffraction pattern as a dark film with a slot of equal size cut in it. In Part 6.2.5 of the experiment, you will exploit this principle to measure the width of a hair. If the distance between the first spot and the central minimum is s = 0.7 cm, L = 12 m, and λ = 6 x 1 0 ^− 7 , what is the width of the hair (mm)?

Answer 1

Explanation:

It is given that,

The distance between the first spot and the central minimum is, s = 0.007 cm

Length, l = 12 m

Wavelength, $\lambda=6\times 10^{-7}\ m$

We need to find the width of the hair. Using the condition of diffraction pattern as :

$s=\dfrac{m\lambda l}{d}$, d is the width of the hair

$d=\dfrac{m\lambda l}{s}$

$d=\dfrac{1\times 6\times 10^{-7}\times 12}{0.007}$

d = 0.00102

or

$d=1.02\times 10^{-3}\ m$

So, the width of the hair is $1.02\times 10^{-3}\ m$. Hence, this is the required solution.