Physics | Light and sound

Physics Study Notes: Light and Sound (The Wave Chapter)

Hello future physicist! Welcome to one of the most exciting chapters in the Waves section: Light and Sound. Don't worry if waves seem confusing—we're going to break down these concepts step-by-step.

You already know that light allows us to see the world, and sound allows us to hear it. But how do these things travel? They travel as waves! Understanding how they behave—reflection, refraction, and speed—is crucial not only for exams but for understanding the technology around us, from fibre optics to ultrasound. Let's dive in!

Quick Review: The Two Types of Waves

Remember, we classify waves based on how their particles vibrate compared to the direction the wave travels:

• Transverse Waves: Vibrations are perpendicular (at 90°) to the direction of energy transfer. Example: Light and all Electromagnetic Waves.
• Longitudinal Waves: Vibrations are parallel (in the same direction) as the energy transfer. They have compressions (squished areas) and rarefactions (stretched areas). Example: Sound.

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Section 1: Light – A Transverse Wave

Light is energy that travels extremely fast! It is part of the Electromagnetic (EM) Spectrum and does not require a medium to travel—which is why sunlight can reach us through the vacuum of space.

1.1 Reflection of Light

Reflection is simply the bouncing back of light when it hits a surface, like looking into a mirror.

Key Terms for Reflection

• Incident Ray: The ray of light heading toward the surface.
• Reflected Ray: The ray of light bouncing off the surface.
• Normal: An imaginary line drawn perpendicular (90°) to the surface at the point where the incident ray hits.
• Angle of Incidence (\(i\)): The angle between the Incident Ray and the Normal.
• Angle of Reflection (\(r\)): The angle between the Reflected Ray and the Normal.

The Laws of Reflection

These two laws are fundamental and always true:

1. The Incident Ray, the Reflected Ray, and the Normal all lie in the same plane.
2. The Angle of Incidence equals the Angle of Reflection.
   (In short: \(i = r\)).

Did You Know? When you look in a flat (plane) mirror, the image you see is Virtual (the light rays only appear to come from that spot) and Laterally Inverted (left and right are swapped).

1.2 Refraction of Light

Refraction is the change in direction of a wave (light or sound) as it passes from one medium to another (e.g., from air to glass).

Why does Refraction happen?

Refraction occurs because light changes speed as it moves into a different material.

Analogy: Imagine pushing a shopping trolley. If the right wheel hits mud first (slowing it down) while the left wheel is still on the smooth floor, the trolley will suddenly turn (change direction).

Rules for Bending

We describe the change in direction relative to the Normal line:

• Air (Fast) to Glass/Water (Slow): The light ray bends TOWARDS the Normal.
• Glass/Water (Slow) to Air (Fast): The light ray bends AWAY from the Normal.

Refractive Index (\(n\))

The Refractive Index (\(n\)) is a measure of how much a material slows down light. The higher the value of \(n\), the more optically dense the material is.

It can be calculated using the speeds of light or the angles (this relationship is called Snell's Law):

1. Using Speed: $$n = \frac{\text{Speed of light in vacuum (or air)}}{\text{Speed of light in medium}}$$

2. Using Angles (Snell's Law): $$n = \frac{\sin i}{\sin r}$$ Where \(i\) is the angle of incidence and \(r\) is the angle of refraction (both measured from the Normal).

Total Internal Reflection (TIR)

When light travels from an optically denser medium (like glass) to a less dense medium (like air), it speeds up and bends away from the Normal.

If the angle of incidence (\(i\)) keeps increasing, eventually the refracted ray will skim along the boundary (angle of refraction = 90°). This angle of incidence is called the Critical Angle (\(c\)).

Total Internal Reflection (TIR) occurs when:

1. The light is travelling from a denser to a less dense medium (e.g., glass to air).
2. The angle of incidence (\(i\)) is greater than the Critical Angle (\(c\)).

TIR is how fibre optic cables work, keeping light trapped inside the cable to transmit data quickly!

You can calculate the critical angle using the refractive index:

$$n = \frac{1}{\sin c}$$

1.3 Lenses and Image Formation

Lenses use the principle of refraction to focus light. There are two main types you need to know:

1. Convex Lens (Converging)

• Shape: Thicker in the middle than at the edges.
• Effect: Causes parallel rays of light to converge (meet) at a single point called the Principal Focus (F).
• Applications: Magnifying glasses, cameras, correcting long-sightedness.

2. Concave Lens (Diverging)

• Shape: Thinner in the middle than at the edges.
• Effect: Causes parallel rays of light to diverge (spread out) as if they came from the Principal Focus.
• Applications: Correcting short-sightedness.

Real vs. Virtual Images

• Real Image: Formed where light rays actually meet. A real image can be projected onto a screen. (Usually formed by a convex lens when the object is far away.)
• Virtual Image: Formed where light rays only appear to meet. Cannot be projected onto a screen. (Images in plane mirrors and images formed by a magnifying glass are virtual.)

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Section 2: Sound – A Longitudinal Wave

Sound is also energy, but unlike light, sound requires particles to vibrate and pass the energy along. This means sound is a mechanical wave.

2.1 Generation and Transmission of Sound

How is Sound Generated?

Sound is always produced by vibrations. When you hit a drum, the skin vibrates. When you speak, your vocal cords vibrate. These vibrations push and pull the surrounding medium (like air) to create waves.

The Importance of a Medium

Sound waves are longitudinal—they require a medium (like air, water, or metal) to travel. The energy is transferred through compressions (high pressure) and rarefactions (low pressure) moving through the material.

Crucial Fact: Sound cannot travel through a vacuum (empty space) because there are no particles to vibrate. This is why explosions in space would be silent!

2.2 The Speed of Sound

The speed of sound depends entirely on the medium it is travelling through and the temperature.

Comparing Speeds

In general, sound travels fastest through materials where the particles are closely packed and tightly bonded (solids), and slowest through gases.

Speed Hierarchy (Fastest to Slowest): $$v_{\text{Solid}} > v_{\text{Liquid}} > v_{\text{Gas}}$$

Example Speeds (Approximate): Steel (~6000 m/s), Water (~1500 m/s), Air (at 20°C: ~343 m/s).

Did You Know? This explains why you see lightning before you hear thunder. Light travels at 300,000,000 m/s, while sound only travels at about 340 m/s!

2.3 Echoes and Distance Measurement

An echo is simply a sound wave that has reflected off a surface and returned to the listener.

Using Echoes to Calculate Speed or Distance

We use the fundamental relationship between speed, distance, and time:

$$v = \frac{d}{t}$$

Where \(v\) is the speed, \(d\) is the distance, and \(t\) is the time taken.

Step-by-Step Echo Calculation:

If you stand 100 meters away from a wall and clap, the sound has to travel 100 m to the wall and 100 m back to your ears.

Total Distance Traveled (\(d_{\text{total}}\)): $$d_{\text{total}} = 2 \times \text{Distance to wall}$$

Example: If you measure the time (\(t\)) it takes for the echo to return, and you know the speed of sound (\(v\)), you can find the distance to the wall:

1. Calculate total distance traveled: \(d = v \times t\)
2. Divide this distance by 2 to find the distance to the reflector (wall).

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Section 3: Connecting Light to the Electromagnetic Spectrum

Visible light is just a tiny slice of the massive family of waves called the Electromagnetic (EM) Spectrum. All waves in the EM spectrum are transverse, travel at the same speed in a vacuum (the speed of light, \(c\)), and transfer energy.

Order of the Spectrum (Increasing Wavelength / Decreasing Frequency)

It is important to know the seven main groups in order.

Mnemonic Aid: Really Many Interesting Visits Under Xtra Great (Rays)

1. Radio Waves (Longest wavelength, lowest frequency)
2. Microwaves
3. Infrared
4. Visible Light (The only part we can see!)
5. Ultraviolet (UV)
6. X-rays
7. Gamma Rays (Shortest wavelength, highest frequency, most energy)

All these waves obey the wave equation: $$v = f \lambda$$ Where \(v\) is the wave speed (which is \(c\) for all EM waves in vacuum), \(f\) is frequency, and \(\lambda\) (lambda) is wavelength.

You did it! Understanding light and sound waves opens up the entire world of optics and communication. Keep practicing those reflection and refraction rules, and you'll master this chapter in no time!