Question

Calculate the resolving power of diffraction grating ruled with 100,000 lines in a distance of 8cm and used in the first order to study the structure of a spectrum line of wavelength 4230 angstrom

Answer 1

Given that,

Number of lines N = 100000

Wavelength $\lambda= 4230\ \AA$

Width = 8 cm

We know that,

The resolving power of diffraction grating is

$R=\dfrac{\lambda}{\Delta\lambda}$

$\dfrac{\lambda}{\Delta\lambda}=nN$.....(I)

We need to calculate the value of $\Delta \lambda$

Using equation (I)

$\dfrac{\lambda}{\Delta\lambda}=nN$

Where, $\lambda$ = wavelength

n = order number

$N =\dfrac{lines}{meter}$

Put the value into the formula

$\dfrac{4230\times10^{-10}}{\Delta\lambda}=1\times\dfrac{100000}{8\times10^{-2}}$

$\Delta\lambda=\dfrac{4230\times10^{-10}\times8\times10^{-2}}{100000}$

$\Delta\lambda=3.384\times10^{-13}\ m$

We need to calculate the resolving power of diffraction grating

Using formula of resolving power

$R=\dfrac{\lambda}{\Delta\lambda}$

Put the value into the formula

$R=\dfrac{4230\times10^{-10}}{3.384\times10^{-13}}$

$R=1250000$

$R=1.25\times10^{6}$

Hence, The resolving power of diffraction grating is $1.25\times10^{6}$.