Question

Consider two gratings. One grating has 3000 lines per cm, and the other one has 6000 lines per cm. Both gratings are illuminated with a beam of the same monochromatic light. Which grating produces the greater separation of colors?Consider two gratings. One grating has 3000 lines per cm, and the other one has 6000 lines per cm. Both gratings are illuminated with a beam of the same monochromatic light. Which grating produces the greater separation of colors?The grating with 3000 lines produces the greater dispersion.

Answer 1

The second grating produces the greater separation

Step-by-step explanation:

In a diffraction grating we have

`dsin\theta=m\lambda\\`

with d:

`d=(1)/(N)`

N : lines/cm

we can compare he separation by takin m as a constant, for example m=1. Hence we have for N=3000 and N=6000:

`sin\theta=N\lambda\\sin\theta=3000\lambda\\sin\theta=6000\lambda\\`

but sin(theta) = y/D (D, distance to the grating)

`y_1=3000D\lambda\\y_2=6000D\lambda`

hence, the second grating produces the greater separation, because lambda and D are constant.

hope this helps!

Answer 2

The grating with 6000 lines produces the greater dispersion

Step-by-step explanation:

Grating is referred to as any regularly spaced collection of identical, parallel and elongated elements.

The relationship between the lines per measurements of gratings and their dispersion is that; the higher the number of grating lines per measurements (which could be centimetres, metres, etc; preferably metres) increases , the smaller and the narrower the maxima becomes. Gratings with a large numbers of lines per measurements are at their peaks and they product a very sharp and accurate wavelength measurements which gives them a greater dispersion compared to gratings with lower lines per measurements.