A student carries out two experiments to investigate the spectra produced from a ray of white light - Scottish Highers Physics - Question 9 - 2015

The speed of light in a medium can be calculated using the formula:

$v = \frac{c}{n}$

Where:

• $v$ is the speed of light in the medium,
• $c$ is the speed of light in vacuum (approximately $3.00 \times 10^8 \; \text{m/s}$),
• $n$ is the refractive index of the medium.

Substituting the values:

$v = \frac{3.00 \times 10^8}{1.54} \approx 1.95 \times 10^8 \; \text{m/s}$

The distance between the slits on the grating can be calculated using the formula:

$d = \frac{m \lambda}{\sin(\theta)}$

Where:

• $d$ is the distance between the slits,
• $m$ is the order of the maximum (for the second-order maximum, $m=2$),
• $heta$ is the angle of the second-order maximum (19.0°).
• $u = f \lambda$ gives orall \lambda = \frac{c}{f}

The wavelength of red light can be determined as:

$\lambda = \frac{3.00 \times 10^8}{4.57 \times 10^{14}}$

$\lambda \approx 6.56 \times 10^{-7} \; \text{m}$

Now substituting values into the formula:

$d = \frac{2 \times 6.56 \times 10^{-7} \; \text{m}}{\sin(19.0^{\circ})} \approx 2.04 \times 10^{-6} \; \text{m}$

The angle to the second order maximum for blue light is different from that for red light because different colors (or wavelengths) of light have different refractive indices. Blue light has a shorter wavelength and is refracted more than red light when passing through a grating or prism. Thus, this leads to varying angles of diffraction for different colors, producing a distinct spectrum.