Snell’s Law is defined as:

n_{i}sinӨ_{i} = n_{R}sinӨ_{R}

…where n_{i} is the index of refraction in the initial medium, Ө_{i } is the angle of incidence, n_{R} is the index of refraction in the refracted medium, and Ө_{R} is the angle of refraction. We can use this formula to find any of the factors in that equation (e.g., what the angle of refraction is or what the index of refraction is for a medium).

Sample Problem:

Light is travelling through air at an angle of 32 degrees and passes into an unknown substance, such that it refracts at an angle of 12.5 degrees. What is the index of refraction of that substance?

To Solve:

List of what we know: ni: 1.00029 (air is always about 1) Ө_{i} : 32 degrees n_{R }: ? Ө_{R }: 12.5 degrees

So we use our equation…

n_{i}sinӨ_{i} = n_{R}sinӨ_{R}

Then we isolate the variable we’re solving for…

n_{i}sinӨ_{i} = n_{R}sinӨ_{R}

——– ——–

sinӨ_{R} sinӨ_{R }

n_{R} = n_{i}sinӨ_{i}

———

sinӨ_{R}

Now we can plug in the values…

n_{R} = (1.00029sin32)

————–

sin12.5

n_{R} = 2.44 (approx.)

If we then refer to a table with given indexes of refraction, we can also determine that the substance is diamond.

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