Relationship between image distance and object for a plane mirror

Plane mirror - Wikipedia

relationship between image distance and object for a plane mirror

You see a point on an object when your eye detects rays of light diverging from For a plane mirror, the image distance is equal to the object distance; that is. Unity. The image is the same distance from the miror as the subject, just on the other side. In the case of plane mirrors, the image is said to be a virtual image. plane mirror images pertains to the relationship between the object's distance to the mirror.

relationship between image distance and object for a plane mirror

The middle photo was taken from above the mirror, looking towards the lamp and screen. A larger version of this photo is shown at right. In this version, the top half of the photo have been brightened, while the bottom half has been darkened, to show better the details of the lamp and to make it more obvious that the image is inverted. Note that rays of light really do meet at the position of this image, which is why we call it a real image.

An incandescent lamp is the object. Its real image is projected on a screen via a concave mirror. Here the light really does fall on the screen to form the image, which is therefore a real image.

Two white lines on the photo at top right show one light path from object to image.

relationship between image distance and object for a plane mirror

The object and the image are equidistant from the mirror, and this distance is twice the focal length. More about that below. Parabolic reflectors Rays parallel to the axis of a parabola converge at the focus Newtonian telescopes use parabolic mirrors because the parallel light from a single, very distant star is converted by the mirror to a single point—provided that the star lies close to the axis of the parabola.

At the point where the ray strikes the mirror, we show the tangent to the mirror and the normal. The angle of reflection equals the angle of incidence. All rays pass through the focus, which in this case is the point 1,0. Fermat's principle states that the path followed by light from one point to another is the path that minimises the time of travel. We've seen above that, if we point a telescope at a very, very distant star, all the light that strikes the mirror point converges at that focus.

Now, if all of those rays cover the distance in minimum time, then that time must be the same for all rays. And, since the speed of light is famously constant, that the distance must be the same. So, if you measure the distance from the right hand side of the picture to the mirror and then to the focus, it is the same for all rays.

If the parallel rays all come from the same very, very distant point, they converge at the focus at the same time. Focussing with a concave mirror A nearly spherical mirror focusses the sun's light on a small area of paper and ignites it.

If this mirror were perfectly parabolic and if it were pointed directly at the sun, then it would focus the radiation onto a very small region near the focal point.

The mirror is not parabolic: We obtained this one cheaply for demonstrations and, for that purpose the aberration it produces is actually useful! This mirror is approximately but not very accurately spherical. We can see in this movie that the shape of the bright image is not even symmetric, so the mirror is not symmetric.

Images Formed by Plane Mirrors - Physics LibreTexts

Nevertheless, by minimising the size of the image formed by the parallel rays of light from the sun, we get a good measure of the focal length. The ignition of the paper is also interesting. After just seven seconds, the paper ignites. It follows that a mirror like this is quite dangerous, especially on a sunny day: How hot can we make an image using a large concave mirror?

Suppose that we had a perfectly parabolic mirror. Ray optics tells us that, if perfectly parabolic, it would focus light on a point. The larger the mirror, the more of the sun's radiation it would focus on that very small area: So, with a very small, largely insulated target, larger mirror areas would give more and more power.

What is the maximum temperature we could reach?

2.1: Images Formed by Plane Mirrors

Thermodynamics tells us that there must be a limit: It were possible to heat the target to a higher temperature than that, then we could run a heat engine from the target to the sun: So there must be a catch. And we'll also show how the temperature of an object is related to the wavelengths of radiation it emits see this link for a start.

Converging mirrors are often sections of a sphere, rather than parabolic. The sphere has the advantage that any normal to the mirror is an axis, so it is not important to align the axis with the object. The disadvantage is that a sphere does focus parallel light to a single point. The curves show that, provided a spherical mirror subtends a sufficiently small angle, it approximates a parabola. We saw above that, when focussing with the entire large mirror, the image of the sun was not a point, because of aberration.

The image below shows an arrangement in which we make an image of the incandescent lamp using the entire mirror. The image of the bulb is distorted due to aberration: Using the entire area of the large mirror, whose shape differs from parabolic, we observe aberration in the image. I made a stop by cutting a circular hole in black cardboard.

Image Characteristics

Of course, this reduces the light reflected by the mirror, so the image is also much dimmer. The result is shown below. The stop in front of the mirror reduces its area, which reduces both the aberration and the brightness of the image.

In the images above, the object is positioned at the centre of the spherical mirror, and is thus at a distance of twice the focal length. This produces an image that is also at a distance of twice the focal length. Let's now look at some different distances, then derive equations relating them. The image is now further from the mirror. In the next photo, the object is at a distance greater than two focal lengths 2f.

relationship between image distance and object for a plane mirror

The image now lies between f and 2f. Let's use the geometry of the ray diagrams sketched above to derive an equation relating the object distance p, the image distance q and the focal length f. Apologies readers, I still have a diagram to make up here. Convex mirrors The photographs below show reflections in spherical mirrors: You can compare this with the plane mirror image above.

Object image and focal distance relationship (proof of formula) - Physics - Khan Academy

Convex mirrors are often spherical. Not only will the order of letters appear reversed, the actual orientation of the letters themselves will appear reversed as well.

Of course, this is a little difficult to do when typing from a keyboard. While there is an apparent left-right reversal of the orientation of the image, there is no top-bottom vertical reversal.

If you stand on your feet in front of a plane mirror, the image does not stand on its head. Similarly, the ceiling does not become the floor. The image is said to be upright, as opposed to inverted. Students of Physics are usually quite intrigued by this apparent left-right reversal. And why is the reversal observed in the left to right direction and not in the head to toe direction? These questions urge us to ponder the situation more deeply. Let's suppose for a moment that we could print the name of your favorite school subject on your shirt and have you look in the mirror.

The answer is no! But you don't have to believe it yet. To further explore the reason for this appearance of left-right reversal, let's suppose we write the word PHYSICS on a transparency and hold it in front of us in front of a plane mirror.

relationship between image distance and object for a plane mirror

The letters are written reversed when viewed in the mirror. But what if we look at the letters on the transparency? How are those letters oriented? When viewed from the perspective of the person holding the transparency and facing the mirror, the letters exhibit the same left-right reversal as the mirror image.

The letters appear reversed on the image because they are actually reversed on the shirt. At least they are reversed when viewed from the perspective of a person who is facing the mirror. All this time you thought the mirror was reversing the letters on your shirt.

relationship between image distance and object for a plane mirror

But the fact is that the letters were already reversed on your shirt; at least they were reversed from the person who stands behind the T-shirt. The people who view your shirt from the front have a different reference frame and thus do not see the letters as being reversed.

The apparent left-right reversal of an image is simply a frame of reference phenomenon. When viewing the image of your shirt in a plane mirror or any part of the worldyou are viewing your shirt from the front. This is a switch of reference frames. Object Distance and Image Distance A third characteristic of plane mirror images pertains to the relationship between the object's distance to the mirror and the image's distance to the mirror.