What is meant by the terms (i) diffraction and (ii) interference? A laser produces a beam of red light with a wavelength of 709 nm - Leaving Cert Physics - Question 7 - 2014

Interference is the addition (or meeting) of two or more waves to form a new wave. This phenomenon occurs when waves superpose, leading to regions of constructive and destructive interference.

To calculate the energy of each photon, we use the equation:

$E = hf$

where:

• $E$ is the energy of the photon,
• $h$ is Planck's constant ($6.63 \times 10^{-34} \text{ J s}$),
• $f$ is the frequency of the light.

First, we need to convert the wavelength into frequency:

$c = f \lambda$

Rearranging gives us:

$f = \frac{c}{\lambda}$

Here, $c = 3.00 \times 10^8 \text{ m/s}$ and $\lambda = 709 \text{ nm} = 709 \times 10^{-9} \text{ m}$, so:

$f = \frac{3.00 \times 10^8}{709 \times 10^{-9}} \approx 4.23 \times 10^{14} \text{ Hz}$

Now substituting back to find the energy:

$E \approx (6.63 \times 10^{-34} \text{ J s})(4.23 \times 10^{14} \text{ Hz}) \approx 2.80 \times 10^{-19} \text{ J}$

The sensors in the eye that can respond to single photons are located in the retina. The retina contains photoreceptor cells, specifically rods and cones, that detect light.

1. Laser light has a single wavelength (monochromatic) and is highly collimated, while vapour lamp light emits a range of wavelengths (polychromatic) and is less collimated.

2. Laser light is coherent, meaning the light waves are in phase, whereas light from a vapour lamp is incoherent and lacks a fixed phase relationship.

To derive the diffraction grating formula, consider the path difference between light rays from adjacent slits.

In a diffraction grating, light passing through slits at angle $\theta$ will satisfy:

$d \sin(\theta) = n\lambda$

where:

• $d$ is the distance between slits (grating spacing),
• $\theta$ is the angle of the diffracted light,
• $n$ is the order of the diffraction (integer number),
• $\lambda$ is the wavelength.

This equation can be illustrated with a diagram showing rays emerging from two adjacent slits at angle $\theta$.

Using the grating formula:

$n \lambda = d \sin(\theta)$

Given $\theta = 34.6°$, $n = 2$ (second order), and $\lambda = 709 \text{ nm} = 0.000000709 \text{ m}$:

Calculate $d$:

1. Find $\sin(34.6°) \approx 0.5736$.
2. Then:

$d = \frac{n \lambda}{\sin(\theta)} = \frac{2(0.000000709)}{0.5736} \approx 0.00000249 \text{ m}$

Finally, convert lines per millimetre:

$\text{Lines per mm} = \frac{1}{d \text{ in mm}} \approx \frac{1}{0.00000249} \approx 400 \text{ lines/mm}$

If the laser is replaced by a ray of white light, a spectrum of colors would be observed on the screen. This occurs because white light contains multiple wavelengths, and each wavelength will diffract at different angles, creating a rainbow-like pattern.