Question

Consider two diffraction 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 dispersion?


a.The dispersion cannot be determined without additional information.


b.The grating with 3000 lines produces the greater dispersion.


c.The grating with 6000 lines produces the greater dispersion.


d.Both gratings produce the same dispersion.

Answer 1

Answer:

The 6000 lines produces the greater dispersion.

Explanation:

Given:

One grating has 3000 lines per cm

Other one grating has 6000 lines per cm

For finding which grating produces the greater dispersion,

From the formula of angular dispersion,

   $D = Nn \sec \beta$

Where $N =$ number of lines per cm, $n =$ order of diffraction

Here we can see angular dispersion is directly proportional to the number of lines per cm

So the grating with 6000 lines produces the greater dispersion.

Therefore, the 6000 lines produces the greater dispersion.