Mammoth Memory

Snell's law applies to velocity

You are unlikely to need this at this level, but it would be useful to know.

Although we know that Snell's law is

`(sin\ \i\n\ \theta)/(sin\ \out\ \theta)=(n\ \(out))/(n\ \(i\n))`

the speed of light is also determined by the medium (material) through which it is travelling. Light travels faster in a vacuum than it does in another medium.


Snell's law can also show the ratio of the velocity of light through different mediums compared to its speed through a vacuum.

`(sin\ \i\n\ \theta)/(sin\ \out\ \theta)=(n\ \(out))/(n\ \(i\n))=(v\e\l\o\c\i\t\y\ \g\o\i\n\g\ \i\n)/(v\e\l\o\c\i\t\y\ \g\o\i\n\g\ \o\u\t)`


NOTE: Care is required to remember that velocity going in is above velocity going out NOT the other way around.


So in fact

`(n\ \(out))/(n\ \(i\n))=(v\e\l\o\c\i\t\y\ \g\o\i\n\g\ \i\n)/(v\e\l\o\c\i\t\y\ \g\o\i\n\g\ \o\u\t)`

And if `n(i\n)` is air this becomes

`(n\ \(out))/1=(v\e\l\o\c\i\t\y\ \g\o\i\n\g\ \i\n)/(v\e\l\o\c\i\t\y\ \g\o\i\n\g\ \o\u\t)`

`n\ \(out)=(v\e\l\o\c\i\t\y\ \g\o\i\n\g\ \i\n)/(v\e\l\o\c\i\t\y\ \g\o\i\n\g\ \o\u\t)`

Velocity of a light ray in one medium is different to in another medium this causes refraction.

`n\ \(out)=(v\e\l\o\c\i\t\y\ \g\o\i\n\g\ \i\n)/(v\e\l\o\c\i\t\y\ \g\o\i\n\g\ \o\u\t)`

If we alter the formula to

`(v\e\l\o\c\i\t\y\ \g\o\i\n\g\ \o\u\t)=(v\e\l\o\c\i\t\y\ \g\o\i\n\g\ \i\n)/(n\ \(out))`


Water becomes:

`(v\e\l\o\c\i\t\y\ \g\o\i\n\g\ \o\u\t)` `=(s\p\e\e\d\ \l\i\g\h\t\ \i\n\ \a\ \v\a\c\u\u\m)/1.3`
  `=0.77\ \o\f\ \t\h\e\ \s\p\e\e\d\ \o\f\ \l\i\g\h\t\ \i\n\ \a\ \v\a\c\u\u\m`


Glass becomes:

`(v\e\l\o\c\i\t\y\ \g\o\i\n\g\ \o\u\t)` `=(s\p\e\e\d\ \l\i\g\h\t\ \i\n\ \a\ \v\a\c\u\u\m)/1.5`
  `=0.66\ \o\f\ \t\h\e\ \s\p\e\e\d\ \o\f\ \l\i\g\h\t\ \i\n\ \a\ \v\a\c\u\u\m`


Diamond becomes:

`(v\e\l\o\c\i\t\y\ \g\o\i\n\g\ \o\u\t)` `=(s\p\e\e\d\ \l\i\g\h\t\ \i\n\ \a\ \v\a\c\u\u\m)/2.4`
  `=0.42\ \o\f\ \t\h\e\ \s\p\e\e\d\ \o\f\ \l\i\g\h\t\ \i\n\ \a\ \v\a\c\u\u\m`



So you can see that light travels through diamond at about half the speed of light. 


`R\e\f\r\a\c\t\i\v\e\ \i\n\d\e\x\ \o\f\ \m\e\d\i\u\m` 

`=(s\p\e\e\d\ \o\f\ \l\i\g\h\t\ \i\n\ \a\i\r)/(s\p\e\e\d\ \o\f\ \l\i\g\h\t\ \i\n\ \m\e\d\i\u\m)`

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