What is the minimum number of lines of a grating which resolve the third orderspectrum of two lines having wavelengths of 5890 Å and 5896 Å?

To solve this problem, we need to use the formula for the resolving power of a grating, which is given by:

R = mN

where R is the resolving power, m is the order of the spectrum, and N is the number of lines of the grating.

The resolving power is also given by:

R = λ / Δλ

where λ is the wavelength and Δλ is the difference in wavelengths.

Given that we want to resolve the third order spectrum (m = 3) of two lines having wavelengths of 5890 Å and 5896 Å, we can calculate Δλ = 5896 Å - 5890 Å = 6 Å.

Substituting these values into the formula for the resolving power, we get:

R = λ / Δλ R = 5890 Å / 6 Å R = 981.67

Then, substituting R and m into the formula for the resolving power of a grating, we get:

981.67 = 3N N = 981.67 / 3 N = 327.22

Since the number of lines of a grating must be an integer, we round up to the nearest whole number. Therefore, the minimum number of lines of a grating which can resolve the third order spectrum of the two given lines is 328.