Question

how many lines must a grating have, used in the second order and near 550 nano meter, to resolve two lines 0.1 angstrom apart ?

Answer 1

Answer on Question #58741, Physics / Optics

How many lines must a grating have, used in the second order and near 550 nanometer, to resolve two lines 0.1 angstrom apart?

Solution:

For two nearly equal wavelengths $\lambda_{1}$ and $\lambda_{2}$ between which a diffraction grating can just barely distinguish, the resolving power R of the grating is defined as

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

If N lines of the grating are illuminated, it can be shown that the resolving power in the mth-order diffraction is

$$R = m N$$

Thus, resolving power increases with increasing order number and with increasing number of illuminated slits.

In our case,

$$\frac {\lambda}{\Delta \lambda} = m N$$ $$\lambda = 550 \cdot 10^{-9} \mathrm{m}, m = 2, \Delta \lambda = 0.1 \cdot 10^{-10} \mathrm{m}.$$ $$N = \frac {\lambda}{m \Delta \lambda} = \frac {550 \cdot 10^{-9}}{2 \cdot 0.1 \cdot 10^{-10}} = 27500$$

Answer: 27500.

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