Question

Suppose pure-wavelength light falls on a diffraction grating. What happens to the interference pattern if the same light falls on a grating that has more lines per centimeter? What happens to the interference pattern if a longer-wavelength light falls on the same grating? Explain how these two effects are consistent in terms of the relationship of wavelength to the distance between slits.

Short answer

The primary maxima will shift apart from each other as the number of lines per cm increases. When the wavelength of light is increased, the angle of the primary maxima increases, and one can observe that the angle of diffraction for primary maxima is proportional to the light wavelength and inversely related to the line spacing, or the distance between the lines.

Step-by-step solution

Define diffraction

The spreading of waves as they move through or around a barrier is referred to as diffraction.

Explanation

The primary maxima will shift apart from each other as the number of lines per cm increases, i.e., the angle of the principal maximum will grow.

When the wavelength of light is increased, the angle of the primary maxima increases and the lines move farther from each other.

The relationship between the grating's primary maxima, wavelength, angle, and line spacing is provided by

$\mathbf{\theta sin\lambda }$

As a result, one can observe that the angle of diffraction for primary maxima is proportional to the light wavelength and inversely related to the line spacing, or the distance between the lines. As a result, the above observation is correct.