# How are images formed in a mirror and lens?

I am not able to understand rays coming from a source object are produced back in the mirror world.

It sounds completely realistic and relatable that rays are originated from and object and then reflected through mirror. Then how are the reflected rays produced back the mirror, it's just a plane surface how is this space created? Like producing back rays behind a plane surface doesn't seem realistic to me? Can you help me getting through it?

I am assuming you understood what I want to ask. And now for the lens, refraction is completely realistic but the why we call the point of intersection of refracted ray a image? As in a real life through a magnifing glass if we point on an object its image is formed on the glass itself (I don't know how) then what are we calculating image distance from lens in the lens formula?

• Our lizard brains don't know about mirrors. We are asking: If there wasn't a mirror here, where would the object have to be, to make the light in my eyes look like this? Apr 20, 2023 at 18:04

## 3 Answers

When we talk about the "mirror world" or the image being produced "behind" the mirror, it is actually a conceptual tool to help us understand and locate the position of the image formed by the mirror. In reality, the image is not physically present behind the mirror. Instead, the light rays reflecting off the object are reflected by the mirror and enter our eyes, making it appear as if the image is located behind the mirror. To understand this better, let's consider a simple plane mirror. When light rays from an object strike the mirror, they are reflected according to the law of reflection (the angle of incidence equals the angle of reflection). When these reflected rays enter our eyes, our brain interprets the light as coming from a straight path. Therefore, we perceive the image to be located behind the mirror at a distance equal to the distance between the object and the mirror. This is called a virtual image because it is not formed by the actual intersection of light rays; rather, it is a result of the way our brain processes the reflected light rays.

Something similar happens with a lens. When light passes through a lens, it is refracted (bent) due to the change in the medium (from air to the lens material). The point of intersection of the refracted rays is called the image. In the case of a magnifying glass, the image you see is not formed on the glass itself. Instead, the lens bends the light rays, which then enter your eyes, and your brain processes these rays to form an image. The image distance in the lens formula refers to the distance between the lens and the point where the refracted rays intersect (either virtually or actually). In the case of a magnifying glass, the image you see is typically a virtual image, formed by the apparent intersection of the refracted rays when extended backward. This is similar to the concept of a virtual image in a mirror.

Oh, you are mistaking a smart shortcut with realism. It is not realistic. It is just a physically motivated smart idea to quickly get answers.

It is also obvious that your school teacher failed to properly teach you even simple light reflection off a mirror and refraction through a piece of glass. It is a very simple experiment---teachers should simply just let students do the experiments for themselves and discuss the results.

Take a blank piece of paper and draw a line dividing it into two approximately equal parts. Align the mirror surface to be standing upright perpendicularly to the piece of paper, all of which are lying on a flat table, preferable above a corkboard that you would not feel sad to poke pins into.

At any place in front of the mirror but not too close, and inside the paper, poke a pin as the object to look through the mirror at. This pin should be at one far corner of the paper. Then look through the mirror at that pin, with one eye, the other eye closed. Put a pin near the mirror that looks to you that you are covering the object pin. Put another pin on the paper, nearer your eye, that covers your view of this last pin. Now you can take the pins out and draw a straight line joining the last two pin holes and extend that to reach the line of the mirror. That intersection point can now be connected in a straight line to the object pin's hole. You should be able to derive that the angle of incidence is equal to the angle of reflection, regardless of how big or small you chose the angle to view the object pin is.

Now, the smart next move is to draw a dotted line to extend the viewing line from your eye's position to behind the mirror. It is clear that the light ray did not pass behind the mirror, but the reflected ray, if it were to come in straight lines as light should be doing, should thus be appearing to come from that direction.

If you repeat the procedure with the same object pin position and mirror position, but with different viewing position, you would get another such dotted line behind the mirror, and they will intersect the first dotted line. Since the image seemed to come from both dotted lines, it must be seeming to come from the intersection of those dotted lines. If you do it a third time, you will see that the third line will also intersect at the same place. You can now prove that this point, called the image point, joined by a line to the object pin's point, is a line perpendicular to the mirror, and the distance between the mirror and the image point is equal to the distance between the mirror and the object pin.

This means that we have a good physical reason to talk about the virtual image at the image point, and can quickly get answers to problems if we start any analysis by first finding them and easily drawing straight lines from them. It is easy to prove that such constructions always allow the important mathematical relationships between the incident and reflected rays to come out correct. Very much less work than having to compute the correct behaviour before drawing any lines.

The same idea is then extended to all sorts of situations, refraction being one of them.

If we didn't know that the mirror was there, we'd think that the reflected rays came from behind the mirror. Indeed we can sometimes 'see' a person just like us behind the mirror even when we're aware of the mirror in front of which we're standing. If we draw a diagram showing two or more rays from a single point, O, on the object being reflected, and we produce (extend) the reflected rays backwards behind the mirror, the point, I, where they meet is the point at which we 'see' O when we look in the mirror, because I is the point the rays seem to be coming from, as in our experience light almost always travels in straight lines. I is called the virtual image of O. Here 'virtual' means imaginary. Every point on the object has its own virtual image behind the mirror.

You should now be able to apply this idea of a virtual image to a lens used as a magnifying glass.