Question

An electromagnetic wave is incident normally on a diffraction grating.
A second-order maximum is produced at an angle of 30 to a normal to the grating.
The grating has 5000 lines per cm.
What is the wavelength of the wave?

Answer 1

The wavelength of the wave is $500nm$.

Step by step calculation

Given data:

Order of the diffraction$=2$

Angle of diffraction$=30$°

number of lines per cm$=5000$

To find:

We must find the wavelength of the wave.

Formula to be used:

• $d=$$1/$number of lines per cm

where: $d=$separation between the slits

number of lines per cm $=5000$

• $dsin$θ$=n$λ

Where:θ$=$$30$°(angle of diffraction)

$n=$ 2 (order of diffraction)

λ$=$wavelength of the wave

Solution:

First to find separation between slits we can use the formula:

$d=1/$lines per cm

$d=\frac{1}{5000}$

$=2$×$10^{-4}$cm

$=2$×$10^{-6} m$

Using the formula :

$dsin$θ$=n$λ we can find the wavelength

λ$=dsin$θ$/n$

$=2$×$10^{-6}$×$sin(30)$$/2$

$=1$×$10^{-6}/2$

$=5$×$10^{-7}$

$=500nm$

The wavelength of the wave is found to be $500nm$

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