A narrow beam of light undergoes dispersion when it passes through either a prism or a diffraction grating - Leaving Cert Physics - Question b - 2013

1. Method of Dispersion: In a prism, light is dispersed primarily due to refraction as it enters and exits the prism, causing a spectrum to be formed. In contrast, in a diffraction grating, dispersion occurs through interference patterns as light waves are diffracted, resulting in a series of bright and dark bands rather than a continuous spectrum.

2. Output Appearance: When light passes through a prism, the colors blend smoothly into one another in a continuous spectrum. However, a diffraction grating produces distinct orders of color bands, which can be separated further apart depending on the angle of observation.

An example of light undergoing dispersion is the formation of rainbows. When sunlight passes through raindrops in the atmosphere, it gets refracted and dispersed into its constituent colors, creating a rainbow.

The yellow light of wavelength 589 nm emitted by sodium atoms in a low-pressure sodium vapor lamp is caused by the excitation and subsequent de-excitation of sodium atoms. When electric energy is supplied to the lamp, it energizes the sodium atoms, causing them to absorb energy. When these excited atoms return to their ground state, they release energy in the form of visible light at the characteristic wavelength of 589 nm.

To find the highest order image, we can use the grating formula:

$d imes ext{sin}( heta) = m imes ext{λ}$

where:

• $d$ is the grating spacing (which is the inverse of lines per mm),
• $m$ is the order of the spectrum,
• $λ$ is the wavelength of light.

Given that the grating has 300 lines per mm,

d = rac{1}{300 ext{ lines/mm}} = rac{1}{300000 ext{ lines/m}} = 3.33 \times 10^{-6} ext{ m}

Now substituting the values:

• $λ = 589 \times 10^{-9} ext{ m}$.

For the highest order $m$, the limit is where $\text{sin}( heta) = 1$:

$d = m \times λ$

Thus,

$m = \frac{d}{λ} = \frac{3.33 \times 10^{-6}}{589 \times 10^{-9}} \approx 5.65$

Since $m$ must be an integer, the highest order is therefore $m = 5$.