Question

1. Calculate the least width that a grating must have to resolve the components of D lines (5890 and5896 A0 ) I n the second order. The grating has 800 lines per cm

Answer 1

QUESTION:

Calculate the least width that a grating must have to resolve the components of D lines (5890 and 5896 A) in the second order. The grating has 800 lines per cm

SOLUTION:

Resolvance or "chromatic resolving power" for a device used to separate the wavelengths of light is defined as

$$R = \frac {\lambda}{\Delta \lambda}$$

Where

$$\lambda = \frac {\lambda_ {1} + \lambda_ {2}}{2}$$ $$\Delta \lambda = \lambda_ {2} - \lambda_ {1}$$

For grating resolvance is

$$R = m N$$

where N is the total number of slits illuminated and m is the order of the diffraction.

Hence

$$R = \frac {\lambda}{\Delta \lambda} = m N$$ $$N = \frac {\lambda}{m \Delta \lambda} = 491$$

Hence, the width that a grating must have is $l = \frac{N}{d} = \frac{491}{800} = 0.614 \, \text{cm}$

ANSWER:

0.614 cm