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How many times does the light beam shown in FIGURE $26-59$ reflect from (a) the top and (b) the bottom mirror?

(a) see explanation(b) 4 times

Physics 103

Chapter 26

Geometrical Optics

Wave Optics

Rutgers, The State University of New Jersey

University of Washington

Simon Fraser University

University of Winnipeg

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question nine says, How many times is the light being reflect from a the top and be the bottom years? So Merei appear mere be down here How many times the lightning reflects were shining it this way of 15 degrees. These mirrors are parallel to each other, 68 centimeters apart. Now that tells us, uh, the normal here, this angles 15 degrees. So that means the angle of reflection is also 15 degrees thes two angles air 15 Which means this whole angle is 30 degrees if we're interested in that. But we can actually figure out how far this lightning travels horizontally just by doing a little bit of trick here. We know that this distance is 68 centimeters. I'm going to redraw this trying over here. Excuse me? 68 centimeters over here and then this angle appears 15 degrees. So how How big is that? And so, if we use the tangent of 15 is equal to the opposite side of call, it acts over adjacent 68. We can actually find what axes and 68 tangent 15 is 18.22 centimeters. X equals 18.22 centimeters. Now that's Onley half of this distance, right? So this is 18.22 This is twice that for the whole distance, which is 36.44 So 36.44 However, we do have to be careful. This is 18.22 centimeters here and then it's gonna bounce and it's gonna bounce, and this distance is going to be 36.44 and then this will bounce. And so how? Maney? Let's see, we have 168 centimeters. We had 168 and then we take away 18.22 leaving us with the 150 essentially 149.78 And then we see how maney 36.44 zehren that divide that by 36.44 and we see that there's four from 30. Divide by 36.44 is 4.11 Now we can't have 0.11 Reflections. It misses that mere eso. That means we can have a 36 of 36 at a 36. But the next one Mrs what about this bottom here Well, it's going to have the same thing. We're gonna have 168 centimeters this time. I don't have to take away that 18 but I'm still going because right, it starts here, although it doesn't doesn't catch that one. So I have 100 68 centimeters and I divide this one by 36.44 1 60 Divided by 36.44 is 4.6 again. I can't have 0.6 of a reflection. It doesn't hit at that time, so in both cases it hits the mere four times before it leaves that mere tunnel.

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