KAHIBARO
Table of Contents
Bending of Light at a Boundary
Refraction is the change in direction of light when it passes from one transparent medium into another, such as from air into water or from air into glass. The bending happens because light travels at different speeds in different materials. When the speed changes at the boundary, the direction usually changes too.
You may have seen this effect when a straw in a glass of water looks bent, or when the bottom of a swimming pool appears closer than it really is. These are common examples of refraction.
Why Refraction Happens
Light does not have the same speed in all materials. In empty space, its speed is
$$
c \approx 3.00 \times 10^8 \text{ m/s}
$$
In a material, the speed is smaller, and we write it as $v$. A material is described by its refractive index $n$, defined by
$$
n = \frac{c}{v}
$$
A larger refractive index means light travels more slowly in that medium.
For example, air has a refractive index close to 1, water is about 1.33, and ordinary glass is often around 1.5.
| Medium | Approximate refractive index $n$ |
|---|---|
| Vacuum | 1.00 |
| Air | 1.00 |
| Water | 1.33 |
| Glass | 1.5 |
| Diamond | 2.42 |
When light enters a medium with a higher refractive index, it slows down. When it enters a medium with a lower refractive index, it speeds up.
Important idea: refraction occurs because the speed of light changes from one medium to another.
The Normal Line
To describe refraction clearly, we measure angles from a special line called the normal. The normal is an imaginary line perpendicular to the surface at the point where the light ray hits.
The incoming ray makes the angle of incidence, and the transmitted ray makes the angle of refraction.
Bending Toward or Away from the Normal
The direction of bending depends on whether light is entering a slower or faster medium.
If light goes from a lower refractive index to a higher refractive index, such as air to glass, it bends toward the normal.
If light goes from a higher refractive index to a lower refractive index, such as glass to air, it bends away from the normal.
This can be summarized simply.
| Change of medium | Speed of light | Direction of bending |
|---|---|---|
| Lower $n$ to higher $n$ | Decreases | Toward the normal |
| Higher $n$ to lower $n$ | Increases | Away from the normal |
Rule: entering a higher refractive index means the ray bends toward the normal. Entering a lower refractive index means the ray bends away from the normal.
What Changes and What Stays the Same
When light refracts, not everything changes.
The speed changes because the medium changes. The wavelength also changes. But the frequency remains the same when light crosses the boundary.
Since wave speed is related to frequency and wavelength by
$$
v = f\lambda
$$
if $v$ changes and $f$ stays constant, then $\lambda$ must change.
| Quantity | Changes during refraction? |
|---|---|
| Speed $v$ | Yes |
| Wavelength $\lambda$ | Yes |
| Frequency $f$ | No |
At a boundary between media, the frequency of light stays the same, but the speed and wavelength usually change.
Refraction Through a Glass Slab
When light enters a slab with parallel sides, it bends at the first surface and bends again at the second surface. The emerging ray is parallel to the original incoming ray, but it is shifted sideways.
This is why objects seen through a thick glass block can appear displaced.
Apparent Depth
A very common effect of refraction is apparent depth. An object under water looks closer to the surface than it really is. Light rays from the object bend away from the normal as they leave the water and enter the air. Your eyes trace the rays backward in straight lines, so the object seems higher than it actually is.
Refractive Index and Optical Density
A medium with a larger refractive index is often called optically denser. This does not necessarily mean it has greater mass density. It only means that light travels more slowly in it.
For example, one transparent substance may be optically denser than another even if its ordinary mass density is not larger. In optics, the phrase refers to the behavior of light, not simply to how heavy the substance is.
Everyday Examples
Refraction explains many familiar effects. A spoon in a cup of tea looks bent at the surface. Fish in water are not exactly where they appear to be. Lenses work because of refraction, although the details of lenses belong to another chapter. Rainbows also involve refraction, together with other effects.
Atmospheric refraction also occurs because air density changes with height. Light from stars and the Sun bends slightly as it passes through layers of the atmosphere. This is why the Sun can appear slightly above the horizon even when it is actually just below it.
A Simple Numerical Example
Suppose light travels in water, where $n = 1.33$. Its speed there is
$$
v = \frac{c}{n} = \frac{3.00 \times 10^8}{1.33} \approx 2.26 \times 10^8 \text{ m/s}
$$
So light is still very fast in water, but slower than in vacuum.
If the frequency of the light is unchanged, then the wavelength in water is smaller than in air or vacuum.
Refractive index formula:
$$
n = \frac{c}{v}
$$
A larger $n$ means a smaller speed $v$.
Refraction and Straight Line Travel
Within a single uniform medium, light travels in straight lines. The bending happens at the boundary between different media, or gradually in a medium whose refractive index changes from place to place, such as the atmosphere.
This helps explain why light seems straight most of the time, but changes direction at surfaces like air to glass or air to water.
Final Picture
Refraction is one of the basic ways light behaves. It tells us that light changes speed in different materials, and this speed change causes a change in direction. By watching whether a ray bends toward or away from the normal, we can tell whether it is entering a slower or faster medium.
Core facts about refraction:
$$
n = \frac{c}{v}
$$
Light entering a higher refractive index bends toward the normal.
Light entering a lower refractive index bends away from the normal.
Frequency stays constant across the boundary, while speed and wavelength change.