runny4
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Is Snells law only for light because the equation for the refractive index involves the speed of light?
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runny4
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then why does the equation use the speed of light
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lerjj
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(Original post by runny4)
then why does the equation use the speed of light
The standard form doesn't. Could you please write out what you think is referred to as Snell's law?

Snell's law is typically this:

n_1 \sin (\theta_1) = n_2 \sin (\theta_2)

where n1, n2 are indexes of refraction. They can presumably be defined somehow for mechanical waves like water waves, because all waves refract and there's at least one proof that doesn't rely on the wave being light. In the case of light specifally, the index of refraction os easily understood as the ratio of the speed of light in that material to in vauum:

 n_1 = \dfrac{c_1}{c_0} where c_0 is the speed of light in vacuum.
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runny4
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(Original post by lerjj)
The standard form doesn't. Could you please write out what you think is referred to as Snell's law?

Snell's law is typically this:

n_1 \sin (\theta_1) = n_2 \sin (\theta_2)

where n1, n2 are indexes of refraction. They can presumably be defined somehow for mechanical waves like water waves, because all waves refract and there's at least one proof that doesn't rely on the wave being light. In the case of light specifally, the index of refraction os easily understood as the ratio of the speed of light in that material to in vauum:

 n_1 = \dfrac{c_1}{c_0} where c_0 is the speed of light in vacuum.
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this is the equatin that depends on light and so snells law does as it uses this term n1
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lerjj
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(Original post by runny4)
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this is the equatin that depends on light and so snells law does as it uses this term n1
That's only how the index is defined for light though. I am not aware of how you calculate the index for other waves, but they certainly refract anyway.

* Actually, just thought a bit more, and I'm pretty sure this is correct:

The version of Snell's law that all waves follow is something like this:

 \dfrac{v_1}{v_2} = \dfrac{\sin(\theta_2)}{ \sin ( \theta _1)}

The only important fact is that the angle is related to the ratio of the old speed to the new speed. This is clearly defined for all waves. For light in particular, however, you can do a trick:

Cross-multiply:

 v_1 \sin(\theta_1) = v_2 \sin( \theta _2)

Divide by some speed, say the speed of light:

 \dfrac{c_1}{c_0} \sin(\theta_1) = \dfrac{c_2}{c_0}\sin(\theta_2)

The ratios of the speeds in this expression are now properties of the material, because they talk about the speed in that material relative to some fixed constant. That's a good thing as it's a much easier operational definition that definining indexes using different refractions at different boundaries.
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runny4
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(Original post by lerjj)
That's only how the index is defined for light though. I am not aware of how you calculate the index for other waves, but they certainly refract anyway.

* Actually, just thought a bit more, and I'm pretty sure this is correct:

The version of Snell's law that all waves follow is something like this:

 \dfrac{v_1}{v_2} = \dfrac{\sin(\theta_2)}{\sin(\the  ta_1)}

The only important fact is that the angle is related to the ratio of the old speed to the new speed. This is clearly defined for all waves. For light in particular, however, you can do a trick:

Cross-multiply:

 v_1 \sin(\theta_1) = v_2 \sin(\theta_2)

Divide by some speed, say the speed of light:

[TeX} \dfrac{c_1}{c_0} \sin(\theta_1) = \dfrac{c_2}{c_0}\sin(\theta_2) [/TeX]

The ratios of the speeds in this expression are now properties of the material, because they talk about the speed in that material relative to some fixed constant. That's a good thing as it's a much easier operational definition that definining indexes using different refractions at different boundaries.
thanks
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0le
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I attach a section from Hecht Optics textbook, Chapter 4 which discusses Snel's Law which seems to imply that any wave can be considered, as stated by lerjj.
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runny4
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#8
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(Original post by lerjj)
That's only how the index is defined for light though. I am not aware of how you calculate the index for other waves, but they certainly refract anyway.

* Actually, just thought a bit more, and I'm pretty sure this is correct:

The version of Snell's law that all waves follow is something like this:

 \dfrac{v_1}{v_2} = \dfrac{\sin(\theta_2)}{ \sin ( \theta _1)}

The only important fact is that the angle is related to the ratio of the old speed to the new speed. This is clearly defined for all waves. For light in particular, however, you can do a trick:

Cross-multiply:

 v_1 \sin(\theta_1) = v_2 \sin( \theta _2)

Divide by some speed, say the speed of light:

 \dfrac{c_1}{c_0} \sin(\theta_1) = \dfrac{c_2}{c_0}\sin(\theta_2)

The ratios of the speeds in this expression are now properties of the material, because they talk about the speed in that material relative to some fixed constant. That's a good thing as it's a much easier operational definition that definining indexes using different refractions at different boundaries.
So if the wave was sound would the equation be the same but use 330m's instead of the speed of light?
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lerjj
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(Original post by runny4)
So if the wave was sound would the equation be the same but use 330m's instead of the speed of light?
You could do one of two things:

1. Use data values for the wave speeds in the two media, and use the equation that relates the ratio of the sines to the ratio of the speeds. This is probably what people actually do when it's not light.

2. Attach an 'index' to the material which gives the speeds as some fraction of a reference speed, like with light. You'd probably use 330m/s as that's quite intuitive, i.e. a material with index 2 has a wave speed half the speed of sound in air, and one with index 0.25 has a wave speed four times it. But any value would do.
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