The Resolving Power of a Grating

The resolving power of a grating refers to its ability to separate closely spaced spectral lines. It is a measure of the grating's ability to produce clear and distinct spectra. The resolving power is an important characteristic of gratings and is influenced by several factors. Among the given options, the correct answer is option 'B', which states that the resolving power increases as the total number of lines on the grating increases. Let's understand why this is the case.

Explanation:
1. Definition of Resolving Power:
The resolving power of a grating is defined as the ratio between the wavelength of two closely spaced spectral lines and the minimum separation distance between them, which can still be resolved. Mathematically, it can be expressed as:
Resolving Power (R) = λ / Δλ
where λ is the wavelength of light and Δλ is the minimum separation between two spectral lines.

2. Influence of the Total Number of Lines:
The resolving power of a grating depends on the total number of lines present on the grating. When light passes through a grating, it gets diffracted by the individual lines on the grating. The diffracted light from each line interferes with the light from other lines, producing a pattern of bright and dark fringes known as an interference pattern. The resolving power of the grating is determined by the ability to distinguish these interference fringes.

3. Relationship between Resolving Power and Total Number of Lines:
As the total number of lines on the grating increases, the interference fringes become more closely spaced. This means that the minimum separation distance between two spectral lines, Δλ, decreases. As a result, the resolving power of the grating increases.

4. Explanation using Formula:
From the formula of resolving power, R = λ / Δλ, we can see that as Δλ decreases, the resolving power increases. Since the total number of lines on the grating directly affects Δλ, increasing the number of lines will decrease Δλ and consequently increase the resolving power.

Conclusion:
In conclusion, the resolving power of a grating increases as the total number of lines on the grating increases. This is because a greater number of lines leads to a smaller minimum separation distance between two spectral lines, resulting in a higher resolving power.