Calculating the Speed of Light using Snell's Law

[AlbertRogers1]

Homework Statement

Hi, I am currently working on science fair physics project which involves measuring speeds of light passing through several substances using a green laser. (please note, I am in 8th grade and have not studied trigonomtry.) We already have our angles on graph paper with a normal but we are confused to exactly caluculate the speed of light using Snell's Law. We are wondering if it was possible that someone could clarify for us in simple terms how to use the formula belonging that Snell's Law to calculate the speed of light.
Here are the angles which were formed by the normal line when we shined the laser beam through a square tupaware, with the same point of entry every time! Here are the angles.
The first substance we used was oil:
The angle before entering the substance was: 25 degrees
The angle after the beam enters the substance was: 16 degrees

The second substance was Steak Marinade mixed with water
The angle before entering the substance was: 25 degrees
The angle after the beam enters the substance was:23 degrees

The third substance was blueberry Fuze (a type of drink)
The angle before entering the substance was: 25 degrees
The angle after the beam enters the substance was:22 degrees

Homework Equations

sin(b)=A*sin(a)/B
or:
b = arcsin[A*sin(a)/B]

The Attempt at a Solution

Please. I am in 8th grade doing an 11th grade level project in order to get an A+. The project has been going very smoothly until the math kicks in. Given the information above, please help me set up the math equation!
THANKS
-Albert

 

[anathema]

Hello Albert,

I'm happy to help you with your project. Snell's Law is a fundamental principle in optics that describes the relationship between the angle of incidence and the angle of refraction when light passes through different mediums. The formula for Snell's Law is:

n1*sin(theta1) = n2*sin(theta2)

Where n1 and n2 are the refractive indices of the two mediums, and theta1 and theta2 are the angles of incidence and refraction, respectively.

In order to use this formula to calculate the speed of light, we need to know the refractive indices of the substances you used. These can be found through research or by consulting a table of refractive indices. Once you have the values for n1 and n2, you can plug them into the formula along with the angles you measured.

For example, let's calculate the speed of light in oil using the information you provided. The refractive index of oil is approximately 1.47. So, we have:

1.47*sin(25) = 1*sin(theta2)

Solving for theta2, we get:

theta2 = arcsin[1.47*sin(25)/1]
theta2 = 16.17 degrees

Now, we can use this value of theta2 to calculate the speed of light in oil:

n1*sin(theta1) = n2*sin(theta2)
1*sin(25) = 1.47*sin(16.17)

Solving for sin(25), we get:

sin(25) = 1.47*sin(16.17)/1
sin(25) = 0.425

Now, we can use the inverse sine function to find the value of theta1:

theta1 = arcsin(0.425)
theta1 = 25.24 degrees

Finally, we can use the speed of light in air (which is approximately 3x10^8 m/s) and the value of theta1 to calculate the speed of light in oil:

n1*sin(theta1) = n2*sin(theta2)
(1)*(3x10^8 m/s)*sin(25.24) = (1.47)*(3x10^8 m/s)*sin(16.17)

Solving for the speed of light in oil, we get:

Speed of light in oil = (1.47)*(3x10^8 m/s)*sin(16.17