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Physics Lesson 12.3.6 - Snell's Law Equation on Refraction of Light
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Welcome to our Physics lesson on Snell's Law Equation on Refraction of Light, this is the sixth lesson of our suite of physics lessons covering the topic of Refraction of Light, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
Snell's Law Equation on Refraction of Light
The path of light inside a medium is somehow related to the angle in which the ray enters to that medium. Therefore, there is a relationship between the refractive indexes and the sines of the incident and refraction angles given by an equation known as Snell's Law. The formula used to express mathematically the Snell's Law is
where
- n1 is the refractive index in the incident medium,
- n2 is the refractive index in the refraction medium,
- θ1 is the angle of incidence, and
- θ2 is the angle of refraction
Example 2
A light ray enters from air to water at 300 (sin 300 = 0.5). Calculate the refraction angle of the light ray in water in these conditions. Take the values for the refractive indexes from the previous paragraph.
Solution 2
We have the following clues:
n1 = 1
n2 = 1.33
θ2 = ?
From the Snell's Law, we have
Substituting the values, we obtain
sinθ2 = 0.5/1.33
= 0.3759
Therefore, we obtain for the angle of refraction θ2:
= 220
This is obvious; the angle of refraction is smaller than the angle of incidence because (as stated by the 2nd Law of Refraction) when light passes from a less dense medium to a denser one it approaches the normal line.
How to Find the Values of Critical Angle in Various Media?
We can use Snell's Law to find the values of critical angles in various media. We just have to know the refractive indexes (or the light's speed in those media) and then apply the Snell's Law for θ2 = 900 (sin 900 = 1). Let's consider an example.
Example 3
What is the critical angle when light moves from glass to air? Take the speed of light in glass equal to 200 000 km/s.
Solution 3
First, we must calculate the refractive index in glass. We have:
Now, using the Snell's Law, we obtain
and giving that n1 = nglass = 1.5, n2 = nair = 1, sinθ2 = 1 (because θ2 = 900), we obtain for the sine of the critical angle:
= 1 × 1/1.5
= 0.6667
Therefore, we obtain for the critical angle θ1 of glass-to-air refraction:
= 41.80
You have reached the end of Physics lesson 12.3.6 Snell's Law Equation on Refraction of Light. There are 7 lessons in this physics tutorial covering Refraction of Light, you can access all the lessons from this tutorial below.
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- Check your calculations for Optics questions with our excellent Optics calculators which contain full equations and calculations clearly displayed line by line. See the Optics Calculators by iCalculator™ below.
- Continuing learning optics - read our next physics tutorial: Interference and Diffraction of Light
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