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Predict/Calculate A small vertical mirror hangs on the wall, 1.40 $\mathrm{m}$ above the floor. Sunlight strikes the mirror, and thereflected beam forms a spot on the floor 2.50 $\mathrm{m}$ from the wall.Later in the day, you notice that the spot has moved to a point 3.75 $\mathrm{m}$ from the wall. (a) Were your two observations made in themorning or in the afternoon? Explain. (b) What was the change inthe Sun's angle of elevation between your two observations?

(a) afternoon(b) see work

Physics 103

Chapter 26

Geometrical Optics

Wave Optics

University of Washington

Simon Fraser University

Hope College

University of Winnipeg

Lectures

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ANGLE OF ELEVATION The…

$\bullet$ A beam of light …

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question five says that we have a mere Ah, small vertical mere hangs on a wall. So here's our small vertical near and it's 1.4 meters above the force of floors down here. And then it says, sunlight strikes the mirror and reflected beam forms a spot on the floor, 2.5 meters from the wall. So sunlight comes in, hits the mere bounces off of the mirror and makes a spot on the floor. And they tell us that this distance right here is 2.5 meters, and they also tell us that this distance right here is 1.4 meters, and then it says later in the day, you notice the spot has moved to a 0.3 point 75 meters from the wall. So that means this has got to move out to here, which means this Ray has to move up so that it's reflected further out to the 3.75 meters, and in order for that to be true, that means then that this Sunray had to come in at west steep oven angle, which means the sun. I used to be higher in the sky and now it is lower in the sky. So question A says we're the two observations made in the morning or in the afternoon. Well, son is on the way down. That has to be in the afternoon. And then what was the change in the sun's angle of elevation between the two observations? So now, uh, we have to find some angles here using tricks. So we have the first triangle, um, which has a side of 1.4 in 2.5 and the second triangle, which has sides of 1.4 and 3.75 Now I'm actually interested in it. Says what was the change in the sun's angle of elevation, So the angle of elevation should draw this just a little bit clear. Um is the angle above the horizon, right? And so if I have my normal line, the angle of elevation was originally this angle and then it changed to be this angle, and we want that difference, which is really if we think about it, the angle of incidents and the angle of incidence again later. We want the difference between those, um, that angle and these angles are the same, and they're complementary to this angle. So I'm gonna find the angle here of these two triangles. So I have my first triangle, which is a right triangle that has side 1.4 inside 2.5. And then I'll do that again, which has side one point for inside 3.751 point for 3.75 And I'm going to find this angle and then find it's compliment and this angle and find its compliment. Although I'm just looking for a different someone really matter. And to do that, I'm going to use Thea Arc Tangent opposite over adjacent So Arc Tangent of two point 5/1 2.0.4 and so second Tangent two point 5/1 2.0.4 is 60.75 degrees. And then down here, same thing Arc tangent of opposite 3.75 divided by one point for which is 69.52 degrees. Now I remember I said I wanted the compliment, So if I subtract those from 90 I get 20.48 and also 29.25 degrees, and it's really the difference between these two things that tells me the difference in the elevation of the sun and so I'll just subtract 29.25 minus 20.48 and get 8.77 degrees. 8.77 degrees is the change in elevation of the sun in the couple hours?

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