A periscope (Fig. P36.5) is useful for viewing objects that cannot be seen directly. It can be u

A periscope (Fig. P36.5) is useful for viewing objects that...

Key Concepts

Plane Mirror Reflection

This concept involves understanding that when light reflects off a flat, or plane, mirror, the angle of incidence equals the angle of reflection. As a result, the image appears to be the same distance behind the mirror as the object is in front of it. This principle is fundamental in analyzing how images are formed in systems like periscopes.

Virtual Image Formation

When an image is formed by a plane mirror, the reflected light rays do not actually converge at the point where the image appears; instead, they only appear to diverge from that point. This is what classifies the image as virtual, meaning it cannot be projected onto a screen, but is nonetheless detectable by an observer.

Image Orientation and Lateral Inversion

In the context of a plane mirror, the image retains the same vertical orientation as the object, so it remains upright. However, a key characteristic of images in flat mirror systems is lateral inversion, which means that the left and right sides of the image are reversed relative to the object.

Magnification in Plane Mirrors

Magnification refers to the ratio of the size of the image to the size of the object. For a plane mirror, this ratio is unity (1:1), which implies that the size of the image is exactly the same as the size of the object. This concept is crucial when determining the proportional accuracy of image representations in optical devices.

Transcript

00:01 So we're told that a periscope is a way for people to view objects that are not commonly in view.

00:09 And we're given an example where there's an object given a distance p1 away from your periscope.

00:16 And you have a periscope that has two mirrors separated by a distance of h.

00:23 And you hope to use this periscope to see this person.

00:27 And we're asked a bunch of questions about this periscope and the images that, or the image that is produced as a result.

00:35 So let's walk through this.

00:38 We have our object here, and the object has an object distance away from this first mirror.

00:47 This first mirror, i'll label it m1.

00:52 And then from here you have this mirror that's separated from a second mirror, m2, and then you have that mirror closest to your eye.

01:01 So just to show you what the light goes from here, you have light that bounces off of this object and travels this distance of p1, bounces off this mirror, travel the distance of h, and bounces off, and again hits your eyes.

01:20 So that you see, you see that this, you see, we're able to see the object as the light rays from the object bounced toward your eyes.

01:33 And we're going to see exactly what image you'll see as a result.

01:40 So on our first step, we're going to take a ray of light and we're going to let it go toward this mirror, the first mirror.

01:50 Now, before we reflected to the mirror down below, what would happen if we just had this mirror and what would the image be? where would the image be? well, we know for flat mirrors, if this mirror was directly perpendicular to this object, then the object would produce an image that's exactly p1 away.

02:11 On this side exactly p1 away actually we'll write it down here this is hypothetical because our mirror is slanted and it allows us to reflect light coming in from here down this way and that doesn't have anything to do with our formation of a image or the distance the image distance because that only depends on our object distance flat mirrors.

02:44 So since this mirror is slanted, the light reflects and it heads down here.

02:53 So what happens that it appears that the light is coming from an image directly above so that it connects to the real image.

03:03 So this is your virtual side and this is your real light that's being reflected off the mirror.

03:09 So we just bring this around and that just gives us a image length of p1.

03:17 So if we were just looking at an image here, we would see an image coming from this direction that's p1 away if we were to look at it, look at the mirror.

03:29 An image coming from this direction at p1.

03:31 The reason why it's coming from this direction is because the light reflects downward, it reflects opposite direction.

03:37 So it appears as if a light is emanating from an image here and coming down through the mirror.

03:45 Okay, so now we have this light, if we continue, it's going down here, and then it reflects again.

03:58 So we have the same problem, or same scenario from above.

04:03 The object distance, the object distance from here, if this mirror was flat, you would have an object distance of p1, since you have your image here, your first image here, i'll label this i1.

04:24 You have your first image here, it has the rays from the light appear to emanate from it and travel a distance of p1, and then another distance of h.

04:36 So theoretically, if the mirror was flat, you'd see an image, a second image, p1 plus h away here.

04:59 But since the light is reflected to hit your eyes, it appears there's a light ray that appears, appears to be coming from this direction.

05:09 And that distance is the same as what we found here.

05:15 It's p1 plus h.

05:19 Because all this mirror's orientation does is that it reflects the light.

05:23 It bends the light so that it reaches your eyes.

05:28 And that means that the image is going to be seen from this direction here, seeing like it's coming from the back of this mirror.

05:36 And it has an image distance of p1 plus h.

05:44 Okay.

05:44 So this is our second image.

05:46 This is our first image here.

05:48 So what we can glean from this is that the image, the image distance from the mirror, which is our question for part a is, i'll just put d -i as our image distance, is p1 plus h.

06:18 And you know that because we had an image, we had an object that was p1 away, from our first mirror, which means that we would have an image distance of p1, since flat mirrors produce images that are equidistant as your object.

06:36 And since you have this object that's p1 away, virtually, you add that distance to the to get to this mirror, and then you add the h to get to the second mirror.

06:45 And so that longer distance is the image distance for the second image you see from this mirror here.

06:53 Right says this is the this is the object and this is the image object and the image and you know that that's p1 plus h away so that's for image distance from the mirror closest to your eye now for part b it asks us if this image that we see is virtual and yes it is virtual not real all images produced by flat mirrors are virtual.

07:46 All flat mirror images are virtual here because the only way for you to see an image from a flat mirror is to have it appear as if it's coming from behind the mirror where the image is located or your image is, so it appears as if your image is behind the mirror, which is virtual.

08:09 There's really no image there, but it appears as though it is.

08:13 So all all images from flat mirrors are virtual...

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