water & lucite

[logistic_guy]

What is the critical angle for the interface between water and lucite? To be internally reflected, the light must start in which material?

 

[khansaheb]

What is the critical angle for the interface between water and lucite? To be internally reflected, the light must start in which material?

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem

 

[logistic_guy]

We use Snell’s Law to solve this problem.

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

where \(\displaystyle n_1\) and \(\displaystyle n_2\) are the refractive indices for the two materials.

The Law looks simple but it needs a careful analysis. When we are finding the critical angle, one of the angles must be \(\displaystyle 90^{\circ}\). How to decide? Easy, in the critical angle case we know that light must travel from a more dense medium (higher refractive index) to a less dense medium. So, the material that has the higher refractive index has the critical angle while the other material has the \(\displaystyle 90^{\circ}\) angle.

Let us compare their refractive indices:

Water \(\displaystyle \rightarrow 1.33\)
Lucite \(\displaystyle \rightarrow 1.51\)

Then,

\(\displaystyle 1.51\sin \theta_1 = 1.33\sin 90^{\circ}\)

This gives:

\(\displaystyle \theta_1 = \sin^{-1}\frac{1.33}{1.51} = 61.7^{\circ}\)

As we said earlier in the critical angle case we know that light must travel from a more dense medium. Therefore, the light must start in lucite.