Study Notes: Refraction - The Amazing Bending Light!
Hey everyone! Have you ever noticed how a straw in a glass of water looks bent or broken? Or how a swimming pool seems shallower than it really is? That's not magic, it's Science! In these notes, we're going to explore a super cool property of light called refraction. We'll learn why light bends, how it creates these cool effects, and how we use this idea in amazing inventions like eyeglasses and fibre optics. It's a key part of understanding how we see the world, so let's dive in!
1. What is Refraction? The Big Idea
Imagine you're running on a smooth pavement and you suddenly run onto some thick, wet sand. What happens? You slow down, right? Light does the exact same thing!
Light travels at different speeds in different materials. These materials are called mediums (the plural is media). For example, light travels super fast in the air (a less dense medium), a bit slower in water, and even slower in glass (more dense mediums).
Refraction is the bending of light when it passes from one medium to another. This bending happens because the light changes speed.
Key Terms to Remember
Medium: Any substance that light can travel through, like air, water, or glass.
Transparent: A material that allows light to pass through it clearly.
Refraction: The bending of a light ray as it passes from one medium into another.
Did you know?
Light travels fastest in a vacuum (like outer space) at an incredible speed of nearly 300,000 kilometres per second! Nothing in the universe can travel faster.
Key Takeaway for Section 1
Refraction is the bending of light caused by a change in its speed as it moves between different materials (mediums).
2. The Rules of Refraction (How to Draw it!)
Scientists use ray diagrams to show how light bends. Don't worry, they're easy to understand once you know the rules. First, let's learn some important lines and angles.
Normal: An imaginary line drawn at 90° to the surface where the two mediums meet.
Angle of Incidence (i): The angle between the incoming light ray and the normal.
Angle of Refraction (r): The angle between the bent light ray (after it enters the new medium) and the normal.
The Two Golden Rules of Bending
There are only two main rules you need to remember for which way the light bends:
Rule 1: When light goes from a less dense medium to a more dense medium (e.g., from air into water), it slows down and bends TOWARDS the normal. This means the angle of refraction (r) is smaller than the angle of incidence (i).
Rule 2: When light goes from a more dense medium to a less dense medium (e.g., from water into air), it speeds up and bends AWAY from the normal. This means the angle of refraction (r) is larger than the angle of incidence (i).
Memory Aid!
Here’s a simple trick to remember the rules. Just think "FST" and "SFA":
FST: Fast to Slow, bends Towards the normal.
SFA: Slow to Fast, bends Away from the normal.
Refractive Index: The "Bendiness" Score
Some materials bend light more than others. We measure this with a number called the refractive index. A higher refractive index means the material is more "optically dense" and slows light down more, causing it to bend more sharply.
For example, a diamond has a very high refractive index, which is why it bends light so much and looks so sparkly! Water has a lower refractive index than diamond, so it bends light less.
The Two Laws of Refraction
The two golden rules above tell you which way light bends. Scientists also found two laws of refraction that every refracted ray follows:
First Law: The incident ray, the refracted ray and the normal all lie in the same plane.
Second Law: When light passes from one medium into another, the value of \(\frac{\sin i}{\sin r}\) stays the same (it is a constant), whatever the angle of incidence. This law is also called Snell's law.
Calculating the Refractive Index
When light travels from air into another medium (such as water or glass), this constant is the refractive index \((n)\) of that medium:
\(n = \frac{\sin i}{\sin r}\)
Here \(i\) is the angle of incidence in air and \(r\) is the angle of refraction in the medium. Both angles are measured from the normal. The refractive index has no unit. Light bends towards the normal when it enters the medium, so \(r\) is smaller than \(i\) and \(n\) is always bigger than 1. For example, \(n\) is about 1.33 for water, about 1.5 for glass and about 2.42 for diamond.
Calculator tip: make sure your calculator is in degree mode (it shows "D" or "DEG") before you press sin.
Worked Example 1: Finding the Refractive Index
Question: A ray of light travels from air into a glass block. The angle of incidence is \(40^\circ\) and the angle of refraction is \(25^\circ\). Find the refractive index of the glass.
Answer:
\(n = \frac{\sin i}{\sin r} = \frac{\sin 40^\circ}{\sin 25^\circ} = \frac{0.643}{0.423} \approx 1.52\)
The refractive index of the glass is about 1.52.
Worked Example 2: Finding the Angle of Refraction
Question: Light travels from air into water. The angle of incidence is \(50^\circ\) and the refractive index of water is 1.33. Find the angle of refraction.
Answer:
\(1.33 = \frac{\sin 50^\circ}{\sin r}\)
\(\sin r = \frac{\sin 50^\circ}{1.33} = \frac{0.766}{1.33} \approx 0.576\)
\(r \approx 35.2^\circ\) (use the \(\sin^{-1}\) key on your calculator)
The ray bends towards the normal, as expected: \(35.2^\circ\) is smaller than \(50^\circ\).
Checking the Laws with Experimental Data
In the lab, use a ray box to shine a ray at the centre of the flat side of a semicircular glass block. Change the angle of incidence and measure the angle of refraction each time with a protractor. Here are some sample results for light going from air into glass:
\(i = 20^\circ,\ r = 13^\circ\): \(\frac{\sin 20^\circ}{\sin 13^\circ} = \frac{0.342}{0.225} \approx 1.52\)
\(i = 40^\circ,\ r = 25^\circ\): \(\frac{\sin 40^\circ}{\sin 25^\circ} = \frac{0.643}{0.423} \approx 1.52\)
\(i = 60^\circ,\ r = 35^\circ\): \(\frac{\sin 60^\circ}{\sin 35^\circ} = \frac{0.866}{0.574} \approx 1.51\)
When \(i\) gets bigger, \(r\) also gets bigger, but \(\frac{\sin i}{\sin r}\) stays almost the same (about 1.5). This supports the second law. The small differences come from errors in measuring the angles. If you plot a graph of \(\sin i\) against \(\sin r\), you get a straight line through the origin, and its slope is the refractive index. You can use the same method to find the refractive index of an unknown liquid: pour it into a semicircular transparent plastic box and repeat the experiment.
Key Takeaway for Section 2
Light bends TOWARDS the normal when it slows down (going into a denser medium) and AWAY from the normal when it speeds up (going into a less dense medium).
3. Refraction in Action! Real-World Examples
Now that we know the rules, let's see how they explain the things we see every day.
The Bent Straw Illusion: When you look at a straw in a glass of water, it looks bent at the surface. Why? The light rays coming from the part of the straw that is underwater travel from water (denser) into air (less dense) before they reach your eyes. According to our rules (SFA!), these rays bend away from the normal. Your brain doesn't know the light has bent, so it assumes the light travelled in a straight line. It traces the rays back to a point that is higher than where the straw actually is, making the straw look bent!
Apparent Depth - The Shallow Pool: For the same reason, a swimming pool or a fish in a tank always looks shallower than it really is. The light from the bottom of the pool bends away from the normal as it leaves the water. Your brain traces the light back in a straight line to an imaginary, "apparent" bottom which is much shallower than the real bottom.
Splitting White Light with a Prism
White light (such as sunlight) is really a mixture of many colours. When white light passes through a triangular glass prism, it is refracted twice: once when it enters the prism and again when it leaves. Each colour bends by a slightly different amount, so the colours spread out into a band of colours called a spectrum: red, orange, yellow, green, blue, indigo and violet. Red light bends the least and violet light bends the most. This splitting of white light into different colours is called dispersion.
A rainbow forms in a similar way: raindrops refract and reflect sunlight and split it into its colours. You will learn more about coloured light in the chapter "Electromagnetic spectrum".
Key Takeaway for Section 3
Many common optical illusions, like bent straws and shallow-looking pools, are caused by the refraction of light as it travels from water to air.
4. A Special Case: Total Internal Reflection (TIR)
Total internal reflection is part of the Core in the 2025 curriculum (Extension in the 2017 curriculum). For more details and experiments, see the chapter "Total internal reflection".
This sounds complicated, but it's just a cool trick that happens when light tries to go from a denser to a less dense medium. Sometimes, instead of escaping, the light gets trapped and reflects back inside!
For Total Internal Reflection (TIR) to happen, two conditions MUST be met:
1. Light must be travelling from a denser medium towards a less dense medium (e.g., from glass to air).
2. The angle of incidence must be GREATER than a special angle called the critical angle.
The critical angle is the specific angle of incidence that causes the refracted ray to travel exactly along the boundary (at 90° to the normal). If you increase the angle of incidence even a tiny bit beyond the critical angle, the light doesn't refract out at all—it reflects back in perfectly. It's like a perfect mirror!
Awesome Applications of TIR
Optical Fibres: These are super-thin, flexible strands of glass or plastic. Light is sent down one end, and it hits the inside walls at an angle greater than the critical angle, so it keeps bouncing (totally internally reflecting) all the way to the other end without escaping. This is how we send information for super-fast internet and how doctors use endoscopes to look inside the body!
Prisms in Periscopes: High-quality periscopes and binoculars use prisms instead of mirrors. They use TIR to reflect light perfectly, giving a much clearer and brighter image.
Key Takeaway for Section 4
For Total Internal Reflection, light must go from dense to less-dense AND the angle of incidence must be larger than the critical angle. This traps light perfectly.
5. Using Refraction: Lenses!
Lenses are Extension in the 2025 curriculum. (In the 2017 curriculum, how lenses converge or spread out light and the uses of lenses were Core, while lens ray diagrams were Extension.) For more, see the chapters "Images formed by convex lenses" and "Images formed by concave lenses".
Lenses are just specially shaped pieces of transparent material (like glass or plastic) designed to bend light in a useful way. They are the key to everything from cameras to telescopes to our own eyes!
Convex Lenses (The "Fat-in-the-Middle" ones)
A convex lens is thicker in the centre and thinner at the edges. It causes parallel light rays to bend inwards and meet at a single point. We say it converges light.
Think of it as: A magnifying glass.
Used in: Magnifying glasses, cameras, projectors, and eyeglasses for people who are long-sighted.
Images formed: Can be magnified and are often used to make things look bigger.
Concave Lenses (The "Thin-in-the-Middle" ones)
A concave lens is thinner in the centre and thicker at the edges. It causes parallel light rays to bend outwards and spread apart. We say it diverges light.
Think of it as: Spreading light out.
Used in: Eyeglasses for people who are short-sighted and in peepholes on doors to give a wide view.
Images formed: Always make objects look smaller and upright.
Drawing Ray Diagrams for Lenses (A Quick Guide)
To find out what kind of image a lens will make, we can draw a simple ray diagram. Here’s the basic idea:
1. Draw a ray from the top of the object travelling parallel to the centre line of the lens.
For a convex lens, this ray bends to pass through the focal point on the other side.
For a concave lens, this ray bends as if it came from the focal point on the same side.
2. Draw a second ray from the top of the object that goes straight through the optical centre (the very middle) of the lens without bending.
3. Where these two rays (or their imaginary extensions) cross is where the top of the image will be formed!
Key Takeaway for Section 5
Convex lenses are converging lenses that bring light together and can magnify things. Concave lenses are diverging lenses that spread light apart.