In an experiment a beam of monochromatic light passes through a diffraction grating and strikes a screen - Leaving Cert Physics - Question 7 - 2009

On the screen, a series of bright and dark spots, known as interference fringes, are observed. The bright spots (maxima) occur where the light waves meet in phase, while the dark spots (minima) occur where the waves meet out of phase, leading to destructive interference.

When monochromatic light passes through the diffraction grating, it spreads out into several beams at specific angles due to diffraction. Each slit acts as a source of wavelets, which overlap and interfere with each other. This can be illustrated with a diagram showing wave fronts emerging from the slits, creating regions of constructive and destructive interference.

The formula representing the angle of the bright spots, known as the maxima, can be given by: $d \sin(\theta) = n\lambda$ Where:

• $d$ is the distance between slits,
• $\theta$ is the angle of the bright spot,
• $n$ is an integer indicating the order of the maximum,
• $\lambda$ is the wavelength of the light.

This experiment demonstrates that light behaves as a wave. The formation of interference patterns indicates the wave nature of light, as this behavior is characteristic of waves interacting with one another.

The experiment allows for the determination of the wavelength ($\lambda$) of the monochromatic light used.

To determine the wavelength of light, the following measurements must be taken:

1. The distance between the slits ($d$) of the diffraction grating.
2. The distance from the grating to the screen ($L$).
3. The distance between the bright spots on the screen ($y$). Using these measurements, the wavelength can be calculated using the formula: $\lambda = \frac{d \times y}{L \times n}$