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Hanging Mirror

Patrick Ford
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Hey, guys, let's do an example. Ah, flat mirror hangs 0.2 m off the ground. If a person 1.8 m tall stands 2 m from the mirror, what is the point on the floor nearest the mirror, which we called X that can be seen in the mirror. The geometry for this problem has already set up. All we have to do is use the law of reflection to figure it out. So this light ray is coming up off the ground from this point, encountering the mirror at its lowest point and then leaving in this direction to your eyes. What, you're gonna be here? Okay? What we have to do is use the law reflection to figure out what angle properly, adjust that light race so that it meets you at exactly 1.8 m off the ground. Here's the normal because we always use the normal one measuring angles. So this is our incident angle theta one. And this is our reflected angle theta one prime. And remember that those two are equal now, notice if I were to continue this normal line right here we form a triangle, right? The triangle that we form is 2 m wide. How tall is it? Well, it's not 1.8 m tall because the mirror the bottom of this point right here is 0.0.2 meters off the ground. So it's actually 1.8 minus 0.2, which is 1.6 m. And this angle right here is state of one prime. Okay, which is the angle that we're interested in finding so clearly we could just use trigonometry to find this. We can use the tangent and we can say that the tangent of data one prime is gonna be the opposite edge which is 1.6 m divided by the adjacent edge which is to and that tells us that data one prime is just 51.3 degrees. Okay, so now we know that this angle is 51. degrees. So this angle to is 51.3 degrees. So we have a new triangle right here. Let me minimize myself. We have a new triangle now this lower triangle where this angle the incident angle is 51.3 degrees. This height is 0.2 m and this length is X right. What's this angle going to be? Well, this is what's known as an alternate interior angle to 51. and all alternate interior angles are the same. So this is going to be 51 3 degrees. All right, So once again, we can use the tangent to find what X should be. We could just say then that the tangent of 51.3 degrees equals the opposite, which is 0.2 m divided by the adjacent which is X, or that X is 0.2 over the tangent of 51.3 degrees. And finally, that X is just 0. meters. Okay, Just using geometry and trigonometry, we can answer this question. The crux of the physics is that these angles right here are the same. And that's the law of reflection. All right, guys, Thanks for watching