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A submerged scuba diver looks un toward the calm surface of a freshwater lake and notes that the Sun appears to be $35^{\circ}$ from thevertical. The diver's friend is standing on the shore of the lake. Atwhat angle above the horizon does the friend see the sun?

40 $\mathrm{deg}$

Physics 103

Chapter 26

Geometrical Optics

Wave Optics

University of Michigan - Ann Arbor

University of Sheffield

McMaster University

Lectures

02:51

In physics, wave optics is…

10:02

Interference is a phenomen…

An underwater scuba diver …

02:31

02:07

Sunlight strikes the surfa…

01:09

A scuba diver, submerged u…

01:39

00:38

A scuba diver sees light r…

01:20

(I) A diver shines a flash…

01:40

05:01

$\bullet$$\bullet$ A 1.55 …

02:32

all right, so we have a scuba diver for this problem. It's underneath the water underneath the surface of the water, and he sees the sun an angle of 35 degrees below the vertical that we've placed above his head. And we're wondering if his buddies on the shore I would angle above the horizontal or both. Horizon, does his buddy see the sun? So we have to realize first is that the scuba diver isn't actually seeing a ray of light that's coming directly from the sun. So he's not directly seeing the sun. He's seeing a ray of light that comes from the sun and then refracts through the water. So first we have to figure out what angles are going on in this refraction in order to figure out what angle but the rise in the sonnets. So we're gonna draw our normal line at the point of a fraction. And by having these two vertical lines, we can clearly see that this angle Fada is congruent to this angle, which is gonna be our angle of a fraction as the late great comes from the sun through the water. So you know this angle here is 35 degrees, and now we can set up Snell's law. We know that here the index of refraction of air it was about one in the index of refraction of water is 1.33 but you can find in your textbook let's set up Snell's law. We can say that. And one or the end of air times a sign a fatal one. Just the angle that we're looking for. It's gonna be the angle of incidence here. It's gonna be equal to end, too. The index of refraction of water How was the sine of the angle of refraction? 35. Now, if you plug in our indexes over fraction and solve for theta one, we'll find that state a one is gonna be equal to the universe. Sign of 1.33 or index of refraction of water and to time is the sign of 35 or angle over fraction all the vital about one, and this should give you an angle of 49 0.8 degrees. But that's not the angle that our buddy in the shore is seeing. That's the angle from the vertical being with everybody on the shore is seeing is the angle from the horizontal, this angle phi. But these two angles of his compliments with one another. So you say that 90 minus 49.8 gives you an answer about 40 degrees. That's what our body sees over here. He sees an angle of 40 degrees above the horizon.

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