Question

An element emits light at two nearly equal wavelengths, 577 nm and 579 nm If the light is normally incident on a diffraction grating with 2000 lines/cm., what is the distance between the 3rd order fringes of the two wavelengths on a screen 1 m from the grating?

Answer 1

1.2 mm

Step-by-step explanation:

Distance of 3 rd order fringe from centre

=3\frac{\lambda D}{d}

where λ is wave length of light D is distance of screen and d is separation between two lines

So distance between 3 rd order fringe of two wavelengths

3\frac{D}{d}\left ( \lambda _1-\lambda _2 \right )\\

=\frac{3\times 1\times 2000}{1\times 10^{-2}}\left ( 579-577 \right )\times 10^{-9}m\\

=12\times 10^{-1}mm