A PLANE TRANSMISSION GRATING HAS 45000 LINES. DETERMINE ITS RESOLVING POWER IN THE SECOND ORDER FOR WAVELENGTH OF 5000A.

To determine the resolving power of a plane transmission grating, we can use a specific formula that relates the number of lines on the grating, the order of the spectrum, and the wavelength of light being analyzed. In your case, we have a grating with 45,000 lines and we want to find its resolving power in the second order for a wavelength of 5000 Å (angstroms).

Understanding Resolving Power

The resolving power (R) of a grating is defined as the ability of the grating to distinguish between two closely spaced wavelengths. The formula for calculating the resolving power is given by:

R = n * N

Where:

• R = resolving power
• n = order of the spectrum
• N = total number of lines on the grating

Applying the Formula

In your scenario:

• The number of lines (N) = 45,000
• The order of the spectrum (n) = 2 (since we are looking for the second order)

Now, substituting these values into the formula:

R = 2 * 45000

Calculating this gives:

R = 90000

Interpreting the Result

The resolving power of the plane transmission grating in the second order for a wavelength of 5000 Å is 90,000. This means that the grating can distinguish between two wavelengths that are very close to each other, specifically, it can resolve wavelengths that differ by approximately:

Δλ = λ / R

Substituting the values:

Δλ = 5000 Å / 90000

Calculating this gives:

Δλ ≈ 0.0556 Å

Conclusion

This result indicates that the grating can differentiate between wavelengths that are about 0.0556 Å apart in the second order. Such high resolving power is particularly useful in spectroscopy, where precise measurements of wavelengths are crucial for identifying substances and analyzing their properties.