The bright outline along the edge of a cloud – the ‘silver lining’ – is an example of the diffraction of light in nature - Leaving Cert Physics - Question 8 - 2021

One way to demonstrate diffraction is by conducting a simple experiment using a laser pointer and a single slit. By shining a laser beam through a narrow slit onto a screen, a pattern of light and dark fringes will appear. This pattern result from the interference of the light waves as they spread out after passing through the slit, thus illustrating the wave characteristics of light.

A diffraction grating is an optical component consisting of a series of closely spaced slits or lines. It disperses light into several beams traveling in different directions, created by the interference of the light waves that pass through or reflect from the grating.

The diffraction grating formula can be derived from the condition for constructive interference. If light of wavelength λ passes through a grating with slit separation d, the angles of the diffracted beams can be described by:

1. For constructive interference:
   • The path difference must be an integer multiple of the wavelength: $d imes sin(θ) = nλ$
2. Rearranging gives us: $nλ = d sin(θ)$ where n is the order of the diffracted light.

To find the angular separation, first convert the lines per mm to slit separation:

• The slit separation, d = 1 / 600 mm = 1.67 x 10^-6 m.
• For n = 3, the formula becomes: $sin(θ) = \frac{nλ}{d} = \frac{3 \times 442 \times 10^{-9}}{1.67 \times 10^{-6}}$
• Which gives: $sin(θ) = 0.7956$
• Therefore, the angular separation can be calculated using the inverse sine function.

The distance between the images can be found using the small angle approximation where:

• Distance y = L * tan(θ), with L = 0.5 m.
• Using small angle approximation, which gives: $y \approx L \times sin(θ)$
• Therefore: $y = 50 cm \times sin(θ)$
• Thus, the separation can be evaluated.

(a) If the blue light was replaced with red light, generally a greater angular separation/diffraction would be observed, as red light has a longer wavelength compared to blue light. (b) If replaced with white light, multiple spectra would appear on the screen since white light contains multiple wavelengths, leading to overlapping patterns of colors.

Radio waves have much longer wavelengths compared to visible light. While visible light has wavelengths in the range of approximately 400 to 700 nm, radio waves can range from millimeters to kilometers.

Radio waves have much longer wavelengths than visible light, making the dimensions of a diffraction grating inadequate for causing any significant diffraction effect. The slits are too small relative to the wavelength of radio waves, thus preventing noticeable diffraction.