The actual path of light propagation is to make the light path take the extreme value (minimum value, maximum value or stable value), and the condition of taking the extreme value is that the first-order variation of the light path is equal to zero, which is the mathematical expression of Fermat's principle.

Hemispheric reflex:

The radius of the spherical surface =R, and the light incident on the spherical surface from one end of the diameter q is reflected to the other end of the diameter p, and the optical path:

Because:

So:

According to Fermat's principle:

Solve it, have to? Substitute d to get: light path? , but the maximum value = 2.8r (the minimum optical path is from one end of the diameter to the other end P of Q, and the optical path =2R).

Extended data:

Law of reflection of light:

When (1) light is reflected, the reflected light, the incident light and the normal are all in the same plane. (on the same plane)

(2) When light is reflected, reflected light and incident light are separated on both sides of the normal.

(3) When light is reflected, the reflection angle is equal to the incident angle. (Equal angle)

Summary: When light strikes the surface of an object, part of the light will be reflected by the surface of the object. This phenomenon is called light reflection.

Special circumstances:

At normal incidence, the reflection angle of the incident angle is zero, and the normal, incident light and reflected light are combined into a line.

Two kinds of reflection: specular reflection and diffuse reflection.

1. Specular reflection: parallel rays are reflected by the interface and emitted in a certain direction in parallel, and the reflected rays can only be received in a certain direction (the reflecting surface is a smooth plane).

2. Diffuse reflection: After the parallel light is reflected by the interface, it is reflected in different directions, that is, the reflected light can be received in different directions (the reflecting surface is rough plane or curved surface).

But both specular reflection and diffuse reflection follow the law of light reflection; Diffuse reflection is irregular reflection only because the reflecting surface is uneven, that is, there are some arcs or sharp lines on the uneven surface. Suppose there is a light incident on it, and its tangent is a plane as a reflection line, then there are many small "mirrors" to form diffuse reflection.

Note: In the reflection of light, the light path is reversible.

Baidu Encyclopedia-Fermat Principle