Question

In the experiment, you will determine the wavelength of a laser by shining the laser beam on a diffraction grating, a set of regularly spaced lines. If the screen is 10 m away, the spots are 5.4 cm apart, and the lines of the grating are separated by 0.1 mm,
what is (in nm)?

Answer 1

Answer:

The wavelength is 539 nm.

Explanation:

Given that,

Distance of screen L= 10 m

Width s= 5.4 cm

Grating separation d= 0.1 mm

Suppose the pattern is displayed on a screen a distance L from the grating and the spots are separated by s. we need to find the wavelength.

The angle between the central and first maximum is given as

$\tan\theta=\dfrac{s}{L}$

$\theta=\tan^{-1}\dfrac{s}{L}$

$\theta=\tan^{-1}\dfrac{5.4\times10^{-2}}{10}$

$\theta=0.309$

We need to calculate the wavelength

The condition for maximum of a diffraction grating is

$d\sin\theta=m\lambda$

$\lambda=\dfrac{d\sin\theta}{m}$

Put the value into the formula

$\lambda=\dfrac{0.1\times10^{-3}\times\sin0.309}{1}$

$\lambda=539\times10^{-9}\ m$

$\lambda=539\ nm$

Hence, The wavelength is 539 nm.