Tuesday, April 10, 2018

optics - What is Snell's law's main formula?


My book states it as $(\sin i)/(\sin r)=n$. However, University Physics has a different say. It says, $n_{a} \sin a =n_{b} \sin b$. Which of the following is correct?



Answer



The second one is more general.


In general, Snell's law can be stated as:


$n_1Sin(\theta_1)=n_2Sin(\theta_2)$



Where $n_1$ is the index of refraction of the medium of the incident ray, $n_2$ the index of refraction of the medium of the refracted ray, and $\theta_1$ and $\theta_2$ are the angles of the incident and refracted rays, respectively (with respect to the normal plane of refraction).


The first equation you have is a particular case where $n_1=1$, which is approximately the index of refraction of the air (many problems you'll encounter assume the incident ray comes from a medium of air)


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