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Question Video: Locating Images Produced by Concave Mirrors Science

The following figure shows two light rays from the same point on an object that are incident on a concave mirror. The distance that the rays travel from the point to the surface of the mirror is greater than the distance from the center of curvature of the mirror to its surface. A real image is produced. What is the location of the image? [A] At the surface of the mirror [B] At the focal point of the mirror [C] At the center of curvature of the mirror [D] Between the focal point and the center of curvature of the mirror

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Video Transcript

The following figure shows two light rays from the same point on an object that are incident on a concave mirror. The distance that the rays travel from the point to the surface of the mirror is greater than the distance from the center of curvature of the mirror to its surface. A real image is produced. What is the location of the image? (A) At the surface of the mirror. (B) At the focal point of the mirror. (C) At the center of curvature of the mirror. Or (D) between the focal point and the center of curvature of the mirror.

Before we begin, let’s take a closer look at the diagram. Here is the concave mirror, and we can see that its focal point and center of curvature have been marked. We also have two light rays shown in red and blue. Notice that they both originate from the same point on the object here but that they travel in different directions. The ray shown in red travels horizontally at first and is then reflected off the surface of the mirror at an angle. Notice that the reflected red ray travels directly through the mirror’s focal point. The ray shown in blue travels diagonally and is incident on the mirror such that the reflected ray travels back along the same path as the original incident ray. Note that the blue ray passes directly through the center of curvature of the mirror.

In this question, we’ve been asked to figure out where the image is produced by these two rays. To do this, let’s clear some room on screen and remember some information about light rays and concave mirrors. First, recall that concave mirrors can produce both real and virtual images. But here, we were told that a real image is produced. Recall that a real image is formed where light rays intersect or cross paths and that real images formed by a concave mirror are inverted, meaning they are appear upside down. Knowing this, in order to determine where this image is formed, we simply have to determine where the rays cross paths.

Now, don’t be fooled by answer option (A). While it is true that both rays do reflect off of the surface of the mirror, they reflect at different points that are quite far away from each other. So they don’t intersect there. So this isn’t where the image is formed. We should eliminate answer choice (A). Next, (B) says that the focal point, and the red ray does pass through the focal point. But the rays don’t intersect here, so we can eliminate this answer choice.

Similarly, for option (C), the blue ray does pass through the mirror’s center of curvature, but the red ray doesn’t, so they don’t cross paths here. And thus, we should eliminate this option as well. Instead, we can see that the rays cross paths here, in between the center of curvature and the focal point. So we know that option (D) is correct. The image is produced between the focal point and the center of curvature of the mirror.

Remember too that because this is a real image formed by a concave mirror, the image is inverted. That’s why these rays, which originate up here at the top of the object, intersect all the way down here, closer to the bottom of the object, as the image appears upside down.

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