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Warm-Up: Let’s go spearfishing

Light and Snell’s Law: Warm-up

The speed of light in a vacuum is one of the universe’s fundamental constants, measuring approximately 3.0 x 108 m/s. However, the speed of light can vary depending on its medium. For example, the speed of light in a 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:

n=c/v

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). Therefore, the index of refraction (n) is a dimensionless value that is related to how fast light moves in a certain medium. 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.

Think about it:

What is the range of possible values 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’.

A bag filled with water has a chopstick through it. The position of the chopstick is distorted where it passes through the water-filled bag.

 

And this makes spearfishing difficult. Below is a schematic of Physics Girl’s most recent spearfishing trip.

A schematic of physics girl on the right, in a boat floating above the water. She looks down into the water at an incident angle labelled theta subscript inc. This angle is measured relative to a vertical line drawn from where her eyes meet the water. To physics girl, the fish's apparent location follows her line of sight, whereas the real fish's location is at a smaller angle measured from the vertical line, labelled as theta subscript ref. This showcases the refractive behaviour of light as physics girl is above the water and the fish is underwater.

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,

n_1\sin\theta_1 =n_2\sin\theta_2

Think about it:

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.

A brief history of optics:

Snell’s Law is named after the Dutch astronomer Willebrord Snellius who wrote this equation in 1621, however, this law actually goes back to at least 984, when the Persian scientist Ibn Sahl used it to calculate the shape of lenses! Fast forward to 2018, our McMaster Alumna Prof. Donna Strickland became the third woman to win the Nobel Prize for Physics for her work in optics.

In the following exercises, you will measure n and learn how to obtain the angle of refraction of light as it passes through different media.

Before you continue!

Make sure you are familiar with Snell’s Law and refraction, as these concepts will be used in the later exercises.

 

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Physics 1A03 - Laboratory Experiments Copyright © by Physics 1A03 Team is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, except where otherwise noted.

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