Problem

Two rays of light converge toward each other, as …

01:40

Problem 15 Medium Difficulty

Predict/Calculate You hold a small plane mirror 0.50 $\mathrm{m}$ in front of your eyes, as shown in FlGURE $26-61$ (not to scale). The mirror is
0.32 $\mathrm{m}$ high, and in it you see the image of a tall building behind you. (a) If the building is 95 behind you, what veight of
the building, $H,$ can be seen in the mirror at any one time? (b) If
you move the mirror closer to your eyes your answer to part
(a) increase, decrease, or stay the same? Explain.

Answer

(a) 61 $\mathrm{m}$
(b) increase

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Video Transcript

question 15 says you stand 95 meters in front of the building. The mere that you're holding 950.5 meters in front of your face is 0.32 meters high and you can see the image of the building behind you. And what they want to know is what height of the building can you see? Um And then part b of this says if I move the mere close to my eyes, does my answer to that increased decrease or stay the same and we'll look at both of those. So for party, we want to find that height. Eso we have light that can come off of the building, hit the mirror and then bounce off the mirror into your eye. I'm going to draw in a couple pieces here that are not really there, but I'm gonna help us make similar triangles. So if this light ray at night that mirror to continued, you would have come to a point directly behind the mere in line with your eye. Um, and what we would have here are similar triangles, So this would meet 0.5 meters out here. Now, What that tells me is if I have this green triangle. It's similar to the overall triangle back here. And so if I confined this distance, I can relate it to that distance. Well, I know that distance. That's half of the mirror. So this why one is 16 centimeters or 160.16 meters. Why two is half the height of the building? Don't know what that is. But why? I wonder why, too has to be the same thing as, um the whole distance of this side, which is 95.5 meters. That's down here 95.5 meters to just this 0.5 meter triangle here. So if I'm gonna do that, I can solve for Y two. So I have 20.16 times 95.5 0.5 equals 0.5 y two, and we'll go ahead and solve this for why? Two point on six times 95.5, divided by 0.5 is 30.56 Why two equals 30.56 meters now. That's only half the height of the building. We could do exactly the same process and we would find the height that we would see that here the other white to so all we have to do is double that. So two y two equals h times two and we see 61 0.12 meters. We can see about 61.1 meters of that building. Now, part B on this says what happens if I move the mirror closer to my eyes so I don't move, but I move the near a little closer. Let me grab another color here. Growth purple. What said put them near here. Now White has to enter my I like this. But remember, the angle of incidence and the angle of reflection are equal. So that means this has got steeper. And so I'm gonna actually be able to see higher on the building and same thing down here. Angle, incidence, angle, reflection. This is also going to get steeper, and so I'll actually be able to see more of the building

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