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 the 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. It can be calculated using the formula:

R = n * N

Where:

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

Plugging in the Values

In your scenario:

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

Now, substituting these values into the formula gives us:

R = 2 * 45000

Calculating the Resolving Power

Now, let’s do the multiplication:

R = 90000

Final Result

The resolving power of the plane transmission grating in the second order for a wavelength of 5000 Å is 90,000.

Why This Matters

A higher resolving power indicates that the grating can distinguish between wavelengths that are very close to each other. In practical terms, this means that with a resolving power of 90,000, the grating can effectively separate spectral lines that are very close in wavelength, which is crucial in applications like spectroscopy where precise measurements are necessary.

In summary, the resolving power of your grating is a significant factor in its ability to analyze light, and understanding how to calculate it helps in various scientific and engineering applications. If you have any further questions about this topic or related concepts, feel free to ask!