Question

When hydrogen is heated or subjected to an electric discharge, it emits light with specific visible wavelengths. A diffraction grating having a spacing between adjacent lines of 4926 nm is used in an experiment to study the visible spectrum of hydrogen. The hydrogen light is sent through the grating and the light emitted by the hydrogen at 656 nm is observed. At what angle does the fourth order bright fringe occur for this specific wavelenth of light occur?

Answer 1

To solve this problem we will apply the concepts related to the double slit-experiment. For which we will relate the distance between the Slits and the Diffraction Angle with the order of the bright fringe and the wavelength, this is mathematically given as,

$d sin\theta = m\lambda$

Here,

d = Distance between Slits

m = Order of the fringes

$\lambda$ = Wavelength

$\text{Spacing between adjacent lines}$ = $d = 4926nm$

$\text{Wavelength of light} = \lambda = 656nm$

Rearranging to find the angle,

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

$\theta = sin^{-1}(\frac{m\lambda}{d})$

$\theta = sin^{-1}(\frac{(4)(656*10^{-9}m)}{4926*10^{-9}m})$

$\theta = 32.19\°$

Therefore the angle that the fourth order bright fringe occur for this specific wavelenth of light occur is 32.19°