ce-jurassic-park-a-t-rex-chases-the-heroes-of-steven-spielbergs-jurassic-park-as-they-desperately-tr

Question

CE Jurassic Park A $T$ rex chases the heroes of Steven Spielberg's Jurassic Park as they desperately try to escape in their Jeep. The T.
rex is closing in fast, as they can see in the outside rearview mirror.
Near the bottom of the mirror they also see the following help-
ful message: OBJECTS IN THE MIRROR ARE CLOSER THAN THEY
APPEAR. Is this mirror concave or convex? Explain.

William Affel · Accepted Answer

all right. So this problem, we have a rear view mirror with some text written in it, and the text reads, Objects in the mirror are closer than they appear. And from that text, we want to deduce whether or not the mirror is con cave or convex on the way. We&#x27;re going to do that as we produce two key pieces of information from the text. First, the fact that objects in the mirror are closer than they appear means that objects in the mirror must also be taller than they appear. So if the mirror is making objects look shorter than its magnification, must be less than one. An important piece of information introduce another important piece of information. Introduces that the magnification is positive because we&#x27;re having a look into the mirror to see a virtual image. So the image must be upright, your erect, another piece of information. One introduces that Dio is positive since within the problem, you really object that we are reflecting off the mirror and then using these three pieces of information were to find a relationship between Dio and D I and that will be able to help us find a sign of f introduced whether the mirror is contractor Khan case, let&#x27;s do that or say that em is equal to negative. D I over dio so thusly d o m must be equal to negative d I So what does this tell us? If m is less than negative one, right, That means Dio must be greater than D I if we also know Do Dio to be positive and m to be positive d I must be negative so you can rewrite this inequality Appear to say Dio is greater than be I or negative d I So then we can write the inverse of these two as well We can say that if Dio is greater than that of d I one over Dio must be less than one over negative d I you might be able to see where we&#x27;re going with this because now we&#x27;re gonna use the lens equation in order to find out the sign of F. So we&#x27;re going to say that if one over dio is less than 11 over negative d i than one over d eyes greater So our difference here must end up being negative and one over F ends up being negative. This tells us that our lens is are mere. Excuse me is convex. It&#x27;s all convex mirrors have negative focal lengths, and that&#x27;s the answer.

Nick Auwerda · Answer

Question 17 says astronomers often use large mirrors in their telescopes to gather as much light as possible from faint, distant objects. Should the Miers B. Khan Cavor Convex? The answer to this is Con Cave. Now let&#x27;s look at why. If we have a convex mirror and we have light coming in from a distant object and it hits the convex side of the outward bulging side, that light is going to reflect out, Uh, this woman comes straight back. This one&#x27;s gonna go out this way, right? Because if we draw our surface, that&#x27;s tangent on the draw and normal to that, this is going to scatter white. Now this will make a virtual image, but that virtual image will be reduced in back here. And we&#x27;re not trying to make things smaller with our telescopes, trying to make things larger. So if we bring in light from the other side, if we use a con cave near, we bring in light and that&#x27;s actually gonna focus it to a point. And that&#x27;s going to give us a really image that we can project onto a screen or more into our eye on. And we&#x27;re going to gather light with a con cave mere, whereas a convex mirror stater&#x27;s light

Katie Mcalpine · Answer

Okay, so in this problem, we are talking about rear view mirrors. Um and we want to know Excuse me. What? Amira&#x27;s radius, If the car is 20 meters away, appear 200.33 times normal size. So it&#x27;s right down the givens. Dio is equal to 20 meters asses like exactly the same Math is the previous problems with different words. Different story behind it. And then, um so just like in the last two problems that I did, you said that you want to say that this is equal to minus D I over Dio and then we want to use the mirror creation one plus whatever D I s one over dio is Do we want the radius for the focal point are So let&#x27;s do this is equal to our over to d I is negative, MD Oh, so let&#x27;s write that down, do that substitution. And then we can solve algebraic plea for our We multiply both sides by d 02 dio and then divide both sides by one minus one over um so now all start to plug in numbers, so that&#x27;s gonna be two times 20. That&#x27;s where iwas divided by one minus one over 10.33 and then you get there. Are is how many sick bags? Three sig, I guess Yes, to think figs. So we get that r is equal to minus 20. So the cockpit of such a large race of curvature of me and said it just barely curb. But in the negative sign means it is convex, So write that down.

Zachary Warner · Answer

While it is true that the images that are produced by convex mirrors are closer to the mirror than the object, the light coming from these convex mirrors is diverge. So these images seem to look smaller than they are. They&#x27;re compressed since they&#x27;re compressed. They took our mind into thinking the objects are farther away than they actually are.

Katie Mcalpine · Answer

So this problem is about their view mirrors. And we&#x27;re told it&#x27;s their con cave. And then they have a certain radius of curvature of 18 centimeters. So I&#x27;ll go ahead, write that down. Let&#x27;s do negative because convex mirrors have negative generally have negative radius of curvature Sze. And then another car is seen in this Samir. And we know this object is 13 meters behind the mirror. So ask equals 13 mirrors. Ah, you know, if I should convert everything this centimeter So 1300 centimeters and the cars one and 1/2 meters tall. So we&#x27;ll say why? It is one and 1/2 meters, and, um, we want to get the height of the image. So let&#x27;s first find the position of the image. Really? He said, totally necessary. The right formula that will just help us find the height. I don&#x27;t think there is, but maybe Yeah, no, I don&#x27;t see any. Yeah, we just want the s and why we want to get the white crime without s prime. I&#x27;m just gonna look through just a little bit more. Uh, I don&#x27;t see any. Okay. It&#x27;s okay. We could just calculate it. So first let&#x27;s get s prime so we can use our over to is equal to one over us, plus one over as prime. And then we got one over s prime is equal to two over are minus one over s. So s Prime is just gonna be this thing to the minus one. So if I plug that into a calculator, I&#x27;m gonna pause the video and do that. Okay, so this, I guess, again, it&#x27;s a case for us is, um, much larger than our and so did that. Great, actually, um, I&#x27;m just gonna double check. Yeah, I guess 13 meters seems like a pretty far distance. And then that seems like a really reasonable radius of curvature like triple check. These numbers were transposed correctly. Um huh. Looks right. Okay, so I basically got that. It&#x27;s at the same it. Okay, so passes really large. Then this term basically goes away, at least in comparison, are over, too. And so, um, the position of the image is that basically are over to at least to the amount of sig figs we have. So we can say that it&#x27;s nine centimeters and we know that why, over my prime equals negative s over ass prime. So why prime equals? Why? Negative. Why times us prime over us. And, um So we want to take this nine divided by 1300 multiply it by one and 1/2. So I&#x27;ll go ahead and do that on a calculator. Um, at times, this prime over us assist 1500 centimeters. So then I got 0.1 meters. So basically one centimeter, So 9 1300 times. 1.5. Great. And now we want to address the more qualitative question. Um, so they&#x27;re closer than they appear. Um, maybe it&#x27;s because you&#x27;re so if it were for a plain mirror, it would just appear, um, it would appear, actually, let me pause and think about this and before I answer it, Okay, Um, after a further inspection, I realized I made a slight mistake in my calculation. And then 2 to 6 figs. Um, this should be 8.9. So I forgot to make the the are negative. So let me go ahead and fix that. And then I can add another significant This How many work prosecutors were we actually given? I think it was too it&#x27;s the lowest. So then this should be, um one point. Oh, son. Um, uterus. I&#x27;ll just write it that way. And just to be totally clear, and then the objects appear are actually closer. I guess you would think if they were really small than they would be really far away, but they&#x27;re actually small because of the curvature of the mirror.

Kyle Godbey · Answer

question over eighteen tells us that we have some rear view mirrors that produce images of cars at our rear that are smaller than they would be if they were flat. So the question asked first, Are they con que ver con facts? And then and ask us to do an actual practical calculation? Well, we know that the mirror must be convex right off the bat because, well, that&#x27;s an awful ex, because only convex mirrors can produce images that are upright and smaller than the object. And for the actual problem, we have an object distance of sixteen meters and a magnification of plus zero point three three. We can use this to find the focal length radius of curvature all all of that in turn because it specifically wants another radius of curvature. But we need to first calculate thie image distance so that we can get that. So to do that, we they use the tried and true linds and makers equation. Rearrange some things and solve for R Soft for the focal ink because that&#x27;s what we&#x27;re going to need. And we see that our focal length is going to be dio times d. I divided by Dio plus d I But like I said, we need die. What we have to relate a magnification and an object Distance is the formula for magnification being equal to minus D I divided by D&#x27;Oh which tells you that d I is equal to minus m d&#x27;Oh. So then plugging in my nissim d&#x27;Oh in both of these, you get that the focal length is simply indio divided by in minus one. All right, it&#x27;s pretty interesting. Ah, and you, Khun. Now at this point, plug in because we have him and we have the object distance. So finally, our focal length is equal to minus seven point eight eight one meters. And since we want the radius of curvature, which is given by our equals two times the focal length we get that are ready, sir, curvature is minus fifteen point seven six. Or you can put it into the correct significant figures. But this is the value that we were looking for

Problem

CE Predict/Explain If a lens is immersed in water…

Problem 87 Hard Difficulty

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