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?
a. The grating with 3000 lines produces the greater dispersion.
b. The grating with 6000 lines produces the greater dispersion.
c. Both gratings produce the same dispersion.

Answer 1

Answer:

Option B, The grating with 6000 lines produces the greater dispersion

Explanation:

The diffraction ability of the grating is equal to the angular dispersion which depends on the dispersion angle.  

As per the equation  

$\frac{dD}{d\lambda} = \frac{m}{a cos D}$

where

$\frac{dD}{d\lambda}$ represent the angular dispersion, m represents the order, a represent the spacing of the lines with in the grit and D represents the diffraction angle.

As per the equation, angular dispersion is inversely proportional to the number of lines (grit line spacing). Thus, the spacing should be minimum to produce greater angular dispersion.

Hence, option B is correct