If we want a brighter view of the telescope, we need more light to reach our eyes through the lenses. Light is refracted and reflected when it passes through any medium, and lens coatings are designed to reduce reflected light and thus increase light transmission. A good telescope will be able to see distant targets even in low light nights. Below I will explain the effect of coatings on light transmission at the level of mathematical principles.

1) Reflected light
When light passes through the front and back surface of a lens, not only refraction but also reflection occurs. Even air, an invisible medium, is able to reflect light, so we see a blue sky.
2) "Ghost image"
Because the curvature of the front and back surface of the lens is different, and there is a certain amount of reflected light, they will produce internal reflection of light between them. Internally reflected light produces false images, i.e., false image points near the image point of the retina. These false images can affect the clarity and comfort of vision.

3) Glare
The human eye is not perfect, so are all optical systems. The image made on the retina is not a dot, but a blurred circle. Therefore, you see two adjacent points created by two juxtaposed multiple overlapping blur circles. As long as the distance between these two points is large enough, the human eye will produce the perception of two points, but if the two points are too close, then the two blur circles will tend to overlap and be mistaken for one point.
Contrast can be used to reflect this phenomenon and express the clarity of vision.
The formula for calculating contrast is：D＝（a-b)/(a+b)
If the higher the contrast D value, the higher the resolution of the visual system for the two points, the clearer the vision; if the two points are very close, the lowest value of their adjacent parts is closer to the highest value, then the D value is low, indicating that the human eye does not feel clear for the two points, or cannot distinguish clearly.
You do not need to fully understand this formula, you just need to know that the human eye resolution is limited.

‘’

1) Reflected light
When light passes through the front and back surface of a lens, not only refraction but also reflection occurs. Even air, an invisible medium, is able to reflect light, so we see a blue sky.
2) "Ghost image"
Because the curvature of the front and back surface of the lens is different, and there is a certain amount of reflected light, they will produce internal reflection of light between them. Internally reflected light produces false images, i.e., false image points near the image point of the retina. These false images can affect the clarity and comfort of vision.

3) Glare
The human eye is not perfect, so are all optical systems. The image made on the retina is not a dot, but a blurred circle. Therefore, you see two adjacent points created by two juxtaposed multiple overlapping blur circles. As long as the distance between these two points is large enough, the human eye will produce the perception of two points, but if the two points are too close, then the two blur circles will tend to overlap and be mistaken for one point.
Contrast can be used to reflect this phenomenon and express the clarity of vision.
The formula for calculating contrast is：D＝（a-b)/(a+b)
If the higher the contrast D value, the higher the resolution of the visual system for the two points, the clearer the vision; if the two points are very close, the lowest value of their adjacent parts is closer to the highest value, then the D value is low, indicating that the human eye does not feel clear for the two points, or cannot distinguish clearly.
You do not need to fully understand this formula, you just need to know that the human eye resolution is limited.

It can be seen that the transmission of a high refractive index lens will be very low when multiple lenses are stacked without a transmission-enhancing film. In the next section, we will introduce the principle of light transmission through an intensifying film.