Introduction

In this problem, we are given the number of lines on a plane transmission diffraction grating, and we need to determine its resolving power in second order for a wavelength of 5000 angstroms.

Given

Number of lines on diffraction grating = 40,000

Wavelength of light = 5000 angstroms

Order of diffraction = 2

Resolving Power

Resolving power is defined as the ability of a diffraction grating to separate two closely spaced wavelengths. It is given by the formula:

R = Nm

Where R is the resolving power, N is the number of lines on the grating, and m is the order of diffraction.

Calculations

- Resolving power in second order:

R = Nm

R = 40,000 x 2

R = 80,000

- Wavelength of light in meters:

5000 angstroms = 5000 x 10^-10 meters

- Separation between two wavelengths:

Δλ = λ / R

Δλ = (5000 x 10^-10) / 80,000

Δλ = 6.25 x 10^-15 meters

Explanation

The resolving power of a diffraction grating depends on the number of lines on the grating and the order of diffraction. In this problem, we are given the number of lines on the grating and the order of diffraction, and we can calculate the resolving power using the formula R = Nm.

Once we have the resolving power, we can use the formula Δλ = λ / R to calculate the separation between two closely spaced wavelengths. This tells us how accurately the diffraction grating can separate two wavelengths.

In this problem, we are given the wavelength of light and we can calculate the separation between two wavelengths using the above formula. The result is a very small value, which indicates that the diffraction grating has a high resolving power and can separate very closely spaced wavelengths.