Snells Law and refractive index

In summary, Snell's Law states that the refractive index of a medium is equal to the ratio of the speed of light in vacuum to the speed of light in that medium. It can also be written as μ1 * sin(angle-1) = μ2 * sin(angle-2) for refraction between two media, and μ1 sin C = μ2 sin 90 for the critical angle of incidence. The mathematical proof for Snell's Law can be derived from various starting assumptions, but the most common one is based on Fermat's principle of least time.
  • #1
jsmith613
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Snells law states that refractive index = (speed in medium 1)/(speed in medium 2)
alternativley
1 μ2 = sin i / sin r

Why therefore does Snells law also equal:

μ1 * sin(angle-1) = μ2 * sin(angle-2)

and for a critical angle


μ1 sin C = μ2 sin 90

thanks
 
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  • #2
Can I split 1 μ2 into μ1/μ2
 
  • #3
jsmith613 said:
Snells law states that refractive index = (speed in medium 1)/(speed in medium 2)
Not quite. Actually,
Refractive index of medium = n (or μ) = (speed in vacuum) / (speed in medium)​
Plus, this isn't Snell's Law , it's the definition of the refractive index.

. . . alternativley
1 μ2 = sin i / sin r
Okay, it looks like you are using μ instead of n for refractive index. Well, the above equation is only true if medium 1 has μ1=1. It's not true in general.

Why therefore does Snells law also equal:

μ1 * sin(angle-1) = μ2 * sin(angle-2)
That is the equation for Snell's Law . Make the following substitutions, and you can get your previous equation:
μ1=1
angle-1 = i
angle-2 = r

. . . and for a critical angleμ1 sin C = μ2 sin 90

thanks
The critical angle (of incidence) occurs when the refracted angle is 90°. Larger angles of incidence would require sin(r)>1 to satisfy Snell's Law, which is impossible.

By the way, the basics of Snell's Law are given here:

https://www.physicsforums.com/library.php?do=view_item&itemid=226
 
  • #4
ok then, so why is Snell's Law as it is. What is the mathmatical proof?

thanks
 
  • #5

1. What is Snell's Law?

Snell's Law, also known as the law of refraction, is a formula that describes the relationship between the angles of incidence and refraction when a light ray passes through a boundary between two different materials.

2. How does Snell's Law relate to the refractive index?

Snell's Law is directly related to the refractive index of a material. The refractive index is a measure of how much a material can bend light, and it is used in Snell's Law to calculate the angle of refraction.

3. What is the formula for Snell's Law?

The formula for Snell's Law is n1sinθ1 = n2sinθ2, where n1 and n2 are the refractive indices of the two materials and θ1 and θ2 are the angles of incidence and refraction, respectively.

4. How does the refractive index affect the speed of light?

The refractive index of a material affects the speed of light by slowing it down as it passes through the material. This is due to the light being bent or refracted, causing it to travel a longer path.

5. Are there any real-life applications of Snell's Law and refractive index?

Yes, there are many real-life applications of Snell's Law and refractive index. Some examples include eyeglasses, lenses in cameras and microscopes, and the design of optical fibers used in telecommunications.

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