### Project Description

# Speed of Light Experiment!

It doesn’t take expensive or sophisticated equipment to carry out a speed of light experiment at home or in the classroom. You can measure the speed of light with nothing but a laser, a protractor and a slab of gelatin, is inexpensive and surprisingly accurate!

**Grades**: 9-12

**Duration**: 45 -60 Minutes

**Supplies**: Classroom Safe Laser Pointer or Laser Blox (red or green), Clear Gelatin, 360 degree protractor

###### NGSS Connections Ps4.A: Electromagnetic Radiation

- Use mathematical representations to support a claim regarding relationships among the frequency, wavelength and speed of waves traveling in various media. (HS-PS4-1)

###### Speed of Light Experiment Background

We know how fast light travels in a vacuum… but what about in other materials? When a light wave hits a boundary between materials, it changes speed. The change in speed depends on the index of refraction of the material the light travels through.

In this experiment, we’ll be measuring the speed of light (a laser beam) as it travels from room air through one or more samples of gelatin.

###### Speed of Light and the Law of Refraction

When a light wave hits a boundary between materials, it changes speed. As a result of this change in speed, it also changes direction or “bends”. This phenomenon is known as refraction.

The **law of refraction,** also known as **Snell’s law, **is a formula that precisely describes how the direction of light changes when it hits a boundary (like from air to gelatin).

Snell’s law can help us with measuring the speed of light by solving the following equation

**Snell’s Law says: Sin*** θ _{1}*

**/Sin**

*θ*=_{2}*v*/_{1}*v*/_{2 = }n_{1}*n*_{2}**Sin***θ*_{1}**/Sin**describes the change in the angle between the incident light beam (laser moving through air in our case) and the surface normal (in our case, the edge of the gelatin)*θ*_{2}*v*_{1}**/**describes the speed of light as it travels from the first material (air) into the second material (gelatin)*v*_{2 }*n*_{1}**/**describes the change in the index of refraction as light travels from one medium (air) into a second medium (gelatin)*n*_{2 }

Therefore:

*θ*is the angle between the incident light beam and the surface normal_{1}*θ*is the angle between the departing light beam and the surface normal_{2}*v*is the speed of light in the first material_{1}**(v**_{air})*v*is the speed of light in the second material_{2}**(v**_{gelatin})*n*is the index of refraction of the first material_{1}**(n**_{air})*n*is the index of refraction of the second material_{2}**(n**_{gelatin})

###### Speed of Light Experiment Procedure

In order to measure the speed of light, we’ll need to solve the equation in two steps.

- First, prepare gelatin – we use Knox plain gelatin. You can prepare as directed on the package – or double the gelatin for a firmer sample. You can also add sugar. The index of refraction will depend on the concentration of gelatin and/or sugar. You may want to prepare two separate samples to compare .

Once gelatin has set, cut out a square/rectangle and place it on a firm, white surface.

- Use the protractor to measure, and record, the angles of refraction (
*θ*,_{1}*θ*)_{2}

Set up Laser Blox , gelatin and protractor so that the incident beam lands on the boundary between gelatin and air at an angle. Measure the angle between the incident beam and normal. This is *θ _{1}*

Measure the angle between normal and the refracted beam in the gelatin. This is *θ _{2}*

**Consider: **Measuring the speed of light depends on accurately measuring the angle from the normal, and this can be tricky. Just remember that if you look directly into a refracting medium, i.e. perpendicular to the surface, the angles are accurate, but if you look off the normal, the angles are distorted. For example, a straight stick thrust into water looks broken at the surface. Therefore, it is important to set up the Laser Blox and protractor properly so accurate readings can be obtained.

- Use your measured values for
and the known quantity index of refraction in air = 1.00029,*θ*_{1 }and θ_{2, }*n*_{1}**n**_{gelatin}

**Sin*** θ _{1}*

**/Sin**

*θ*=_{2}*n*/_{air}*n*_{gelatin}The calculated index of refraction for the gelatin will vary depending on how concentrated it is and how much sugar (if any) you add.

- Now you can use the measured angles of refraction (
**Sin***θ*_{1}**and Sin**and calculated (and known) values for indexes of refraction (*θ*)_{2}*n*_{1}**and**) as well as the known value for the speed of light in a vacuum*n*_{2}**C=299,792,458 m/s**for measuring the speed of light in the medium (gelatin)

*V _{gelatin }=c/n_{gelatin} = (2.99792458 X10^{8 }m/s) /n_{gelatin}*

** **_{ }

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