Why can a cat's eye see the whole outside world?

"Seeing a leopard through a bamboo tube" is an idiom, which means that if you observe a leopard through a small bamboo tube, you cannot see the whole picture of the leopard, but only a spot on its body.

Why can we only see a spot of a leopard when we observe it through a bamboo tube? Because the cross section of the bamboo tube is only so large, so we can only see a piece of image of that size. Similarly, if we drill a small hole in our door, we can only see a little bit of the image outside through this small hole. But if we install a "cat's eye" on this small hole, the situation will be completely different. "Cat's eye", also known as door mirror, is an optical device that allows people to observe the outdoor environment from inside the house, and this small device also fully considers privacy, that is, you can only look out from the house, and the outside cannot see what is happening inside the house.

Why can we only see a glimpse of the leopard through a tube, while a cat's eye can see the whole picture outside the house? Why can't people outside the house look back to see what's going on inside the house?

Generally speaking, the images of objects we see can be divided into two categories, namely real images and virtual images. "Real image", as the name implies, is the real image of the object, which is formed by the convergence of actual light, so the real image can be received by the light screen and presented on the light screen. "Virtual image", as the name implies, is the false image of the object. It is the image presented at the intersection of the reverse extension line of the reflected or refracted light after the actual light is reflected or refracted by the optical element. The virtual image is not the actual light, so the light screen cannot receive it, let alone present it on the light screen. Of course, the reason why people can see virtual images is because light enters the eyes, but these rays do not come from virtual images, but from light reflected or refracted by optical elements.

The images we see through the lens are all virtual images. Through a convex lens, we can see a magnified virtual image, and through a concave lens, we can see a reduced virtual image.

So what is a cat's eye? A cat's eye is actually an optical system composed of two lenses, in which the concave lens acts as the objective lens, which is the side close to the outside of the door, and the convex lens acts as the eyepiece, which is the side close to the inside of the house. Without installing a lens, looking out from the small hole on the door, you can only see a limited image, but after installing a lens, the situation is different. The light will be refracted by the lens, so we can see a wider image.

When the image outside the door passes through the cat's eye, it will first pass through the concave lens, which will diverge the light, and then form an upright and reduced virtual image on the reverse extension line of the refracted light.

Next, this upright and reduced virtual image will pass through the convex lens. The convex lens has the function of converging light, so after the light passes through the convex lens, it will form an upright and enlarged virtual image on the extension line of its direction. Of course, this enlarged virtual image is only for the reduced virtual image presented by the concave lens, which is not as large as the original image of the object. This upright and enlarged virtual image generated by the refraction of the convex lens is the image we see through the cat's eye. Do you think this convex lens is a bit redundant? It seems that it only plays a magnifying role. It seems that it does not affect our overall view of the outside world with or without it. Don't worry, this convex lens actually has another function.

If there is only a concave lens on the cat's eye, then the cat's eye is bidirectional, which means you can observe the outside of the house from inside and peek into the house from outside. So why does the cat's eye become one-way after adding a convex lens?

Let's take a look at what happens if we peek inside the house from outside. Conversely, the image of the object will first pass through the convex lens, and the light passing through the convex lens will converge. However, the focal length of the convex lens is relatively long, so before the image is formed, the refracted light will pass through the concave lens again, and the light passing through the concave lens will diverge, thus forming a positive virtual image directly on the reverse extension line. Isn't it still an image? Can't we see it from outside?

An image is indeed formed, and theoretically it should be visible from outside, but the problem is that the cat's eye is very small, so if you want to see the image inside the cat's eye, you must put your eyes close to the cat's eye, and the focal length of the concave lens is very short, so the image is only 2-3 cm away from the eye.

Here we need to put forward a concept, that is, "the near point of the human eye". The so-called "near point of the human eye" is the closest distance that the human eye can see clearly. Under normal circumstances, this distance is about 10 cm. Obviously, 2-3 cm is too close, so looking at the cat's eye can only be a blur. It can be seen that in the cat's eye optical system, both concave lenses and convex lenses are indispensable. Without a concave lens, you cannot see the vast world, and without a convex lens, the cat's eye will become a two-way observation system, which is embarrassing.

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