Physics : Wave II

Wave nature of light

Reflection and refraction are properties that can be performed by all matters including particles and waves, but only waves perform Interference and Diffraction

Diffraction: Usually we use a slit with width ~10λ to observe diffraction (for visible light, the width is usually 0.1mm). If it’s too narrow there’s not enough energy to pass through, it it’s too wide, no diffraction is exhibited. We can observe the diffraction of red light is more than blue light, so λ_red > λ_blue.

Interference: Young’s double-slit experiment: when light passes through the double-slit, a series of bright and dark fringe is observed.

Note that these experiments has to be done under very dark environment since the slit is so narrow that only a very small amount of energy is given out.

Quantitative interpretation

Consider the diagram; S is the initial source, while S₁S₂ is a double slit (with slit at S₁ and S₂). CX (usually denoted as D, and is 1m if not specified), the distance between two slits is denoted as a(usually 0.1mm). The calculation is based on the assumption that D>>a. Now denote Y_m is the distance from the central maximum to the m^th light fringe, the θ is the red angle. When D>>a, sinθ is approximately equal to tanθ. S₁T and S₂T is assumed to be parallel, so that S₁R is assumed to be the path difference, that is, mλ.

Y_m = Dtanθ = Dsinθ = Dmλ/a = m(Dλ/a). Distance between two successive light fringe = Dλ/a, which is independent of m, this explains why the fringes are equally spread.

Note that the interference is not complete except the central maximum since energy is lost proportional to path travelled, therefore non-zero path difference cause in different A of the two waves that they can’t add/eliminate completely.

Note that it can be used in other waves but the formula is no longer true since other waves has much larger λ, then a has to be much more larger, which makes D>>a no longer true. Also moonlight (single wavelength) source has to be used. If white light is used, then the result will be: white light (central max) – violet (1^st order) – red (1^st order) – violet (2^nd order)…

Plane transmission grating – with many slits

It only allows plane waves (straight waves) and normal to the plane of grating to pass through.

Now consider the m^th fringe, we have asinθ = mλ ≤ a, a/λ ≥ m, [m] is the last order of light fringe that can be observed.

Dual nature of light

In the grating experiment, the interference is limited because for those fringes that beyond the m_max, they do not belongs to the same package of photon produced by the source, so that they’re not coherence and they don’t interfere. This shows the particle nature of light, it can be quantified as photon.

At the same time, it’s a wave, the electromagnetic wave, which composes by perpendicular oscillating electric and magnetic field. It’s transverse waves and transmit energy like other waves. Their travelling speed in vacuum is 3*10⁸ms^-1. By v = fλ, the higher f, the shortest λ.

1)       Radio waves (λ: 10^-1 to 10⁴m) : broadcasting

2)       Microwaves (λ: 10^-3 to 10^-1m): heating, radar

3)       Infra-red (λ: 10^-3 to10^-6m), body emission, heat transfer

4)       Visible light (λ: violet 4*10^-7 to red 7*10^-7m) for illumination

5)       Ultraviolet (λ: 10^-9 to 10^-8m), for killing germs, UV light lamp (Hg lamp)

6)       X-rays (λ: 10^-10m) medical dialog (project e^- on heavy metals to produce X-rays)

7)       Gamma ray (λ: 10^-12 m) kill cancer cell, sterilize food.

Sound waves

-          Speed of sound waves depends of nature and density of medium, e.g., 300ms^-1 in air but 1500ms^-1 in solid

-          Produced by longitudinal waves of particle, so it can’t pass through vacuum.

-          Detected by cathode ray oscilloscope (CRO) and microphone.

-          Exhibits properties of wave, e.g. refraction by a CO₂ balloon.

-          Loudness of sound in terms of decibel (dB), 0dB is the threshold of hearing while 120dB is the threshold is pain. Audible sound pitch: 20-20000Hz (Note that there exist negative dB but human can’t hear it.)

-          Loudness depends on A, pitch of sound depends on f, quality of sound (note VS noise) depends on the regularity, and main note of a sound depends on the largest single wave produced by the source.

-          Application: detecting sea animals (sonar) since EM waves is absorbed by waters. Also we should use supersonic only since the sound waves with lower frequency diffracts too much so that too many energy is lost. Medical application and cleaning fragile objects.