Question

Referring to Figure 25.57: two different potential paths from point A to point B are shown. Point A is in the air, and point B is in water. For which of these paths (upper or lower) would light travel from point A to point B faster? Which of the paths more accurately represents how a light ray would travel from point A to point B? Explain.

Question Image

**Figure 25.57**

Final Answer

upper path.

$\theta_2 \lt \theta_1$

$\theta_2 \lt \theta_1$

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This is College Physics Answers with Shaun Dychko.
A Light Ray is traveling from air into water. So it goes from a medium of index of refraction of 1.00 to a medium with an index of refraction of 1.33 and we can use Snell's Law to verify that the angle of refraction

*Theta two*has to be less than the angle of incidence*Theta One*and so that means this upper path is what the light is going to follow. So*n1 sine Theta One*equals*n2 sine Theta Two*. That's Snell's Law and we can solve for*Theta two*by dividing both sides by*n2*and then we get*sine Theta Two*is*n1 sine Theta One*over*n2*and now since*n2*is greater than*n1*. So the refraction of water is greater than the initial index of refraction in air. That means that this is going to be greater sorry, this is going to be less than*sine Theta One*because*sine Theta One*is getting multiplied by a fraction is less than one because the denominator is bigger than the numerator there. So*sine Theta Two*is going to be less than*sine Theta One*since the denominator*n2*is greater than the numerator factor*n1*and with*sine Theta two*being less than*sine Theta One*that means*Theta Two*is less than*Theta One*and that's true for this upper path.