Warm-Up: Let’s go spearfishing
Light and Snell’s Law: Warm-up
The speed of light is one of the universe’s fundamental constants when it travels in a vacuum. The speed of light in a vacuum is approximately 3.0 x 108 m/s. However the speed of light can vary in a medium, for example the speed of light in vacuum is not the same as the speed of light in glass. A parameter that describes how much a medium slows the speed of light is the Index of Refraction:
In this equation, c is the speed of light in a vacuum, and v is the speed of light through a medium (like air or water). For reference, the refractive index of air is nearly n = 1, while the refractive index of glass is around n = 1.5 – 1.9. Some materials (like diamond) have an index of refraction greater than 2.
What range of values are possible for an Index of Refraction? Can you have n < 1?
A consequence of light having different speeds in different media is that the trajectory of the beam will be bent, or “refracted”.
And this makes spearfishing difficult. Below is a schematic of Physics Girl’s most recent spearfishing trip.
You will notice the light maintains a straight trajectory in both air and water, but at the boundary of two media, will bend by some angle (the long dashed lines). This creates an “apparent location” of the fish that Physics Girl sees (the dotted line), which is different from the actual location of the fish. In other words, Physics Girl may think her line of sight is perfectly straight, and the fish she sees is at the end of the dotted line. However, because the light is refracted at the air-water interface, the fish she sees is actually in a different spot. The angle of incidence and the angle of refraction, as measured relative to a normal line perpendicular to the surface, are related by the refractive index of each medium, and are described by Snell’s Law,
Snell’s Law is named after the Dutch astronomer Willebrord Snellius who wrote this equation in 1621, but in fact the law goes back to at least 984, when the Persian scientist Ibn Sahl used the law to calculate the shape of lenses! Forward to 2018, when our McMaster Alumna Prof. Donna Strickland is the third woman to win the Nobel Prize for Physics for her work in optics!
Based on the schematic and what you know about indices of refraction, does Physics Girl need to aim above or below the apparent location of the fish to hit it? Hint: n2 > n1.
In the following exercises, you will measure n and learn how to obtain the angle of refraction of light as it passes through different mediums.
Before you continue!
Make sure you understand Snell’s law and refraction, as these concepcts will be used in the later exercises.
