Refraction angle

Physical terms

Collection

zero Useful+1

zero

This entry is made by Compilation and application of scientific encyclopedia entries of "Science Popularization China" to examine.

refraction Light and normal The included angle of is called refraction angle. Its refraction follows Law of refraction 。 When light slants from air into water or other media, the refraction angle is smaller than the incidence angle. When the incidence angle increases, the refraction angle increases. When light slants into the air from water or other media, the refraction angle is greater than the incidence angle. When light is emitted vertically from air (or other media), the propagation direction does not change.

Chinese name: Refraction angle
Foreign name: angle of refraction
Definition: refraction Light and normal Included angle of

Refraction: follow Law of refraction
Application: The position seen is higher than the actual position
Discipline: physics 、 optics

catalog

Introduction to refraction angle

Announce

edit

one Law of refraction of light : three lines on the same surface, normal in the middle, large angle in the air, light path Reversible.

﹙1﹚ Refraction ray The incident light and normal are in the same plane.

(2) Refracted ray and Incident light Separated on both sides of the normal.

(3) When light slants from air into water or other media, the refraction angle is less than Angle of incidence When the incident angle increases, the refraction angle increases. When light slants into the air from water or other media, the refraction angle is greater than the incidence angle. When light vertically shoots into the air (or other media), the propagation direction does not change.

2. Summary of light refraction law:

Schematic diagram of incident light, reflected light and refracted light

(1) Three lines and one side.

(2) The two lines live apart.

(3) The relationship between two angles can be divided into three situations:

① When the incident light is incident perpendicular to the interface, the refraction angle is equal to the incident angle, which is equal to 0 °;

② When light slants from air into water and other media, the refraction angle is smaller than the incidence angle;

③ When light slants into the air from water and other media, the refraction angle is larger than the incidence angle.

3. Application: When looking at objects in the water from the air, or looking at objects in the air from the water, you can see the virtual image of the object, and the position you see is higher than the actual position.

Law of refraction

Announce

edit

The mathematical expression of refraction law is sin i /sin γ = v one / v two

Among them, i yes Angle of incidence ， γ Is the refraction angle, v 1， v two Is the speed of light in both media.

And because vacuum Speed of light in c It is maximum and constant, so we can define a new physical quantity - refractive index to measure the deflection degree of the propagation path of light from vacuum into the medium. Its definition formula is:

n = c / v 。

Among them, n Is the refractive index.

For two different Transparent material , define the deformation of the refractive index formula v one = c / n one ， v two = c / n two Substitute the law of refraction and reduce the speed of light in vacuum c , we have

sin i /sin γ ＝ v one / v two ＝ n two / n one 。^[1] 。

Related derivation

Announce

edit

Derivation by Fermat principle

Fermat principle Also known as the "shortest time principle": light The path of propagation is the path that takes the least time. The more correct version of Fermat's principle should be the "stationary time principle". In some cases, the time required for the path of light propagation may not be the minimum value, but the maximum value, or even the inflection value. For example, for a plane mirror, the optical path of the reflection path of any two points is the minimum; For a semi elliptical mirror, the light reflection path of the two focal points is not unique, and the optical path is the same, which is the maximum and minimum value; For a semicircular mirror, its two endpoints Q、P The optical path of the reflection path of is the maximum value; As shown in the rightmost figure, for a mirror composed of a quarter circular mirror and a plane mirror, the same two points Q、P The optical path of the reflection path of is an inflection value.
Assume that the refractive index of medium 1 and medium 2 are n one 、 n two , light from medium 1 at point O Propagation into medium 2, θ one Is the angle of incidence, θ two Is the refraction angle.
From Fermat's principle, Snell's law can be deduced. By setting the derivative of optical path with respect to time to zero, you can find the "stable path", which is the path of light propagation. The propagation speed of light in medium 1 and medium 2 is v one = c / n one ， v two = c / n two 。 Among them, c Is the speed of light in vacuum.
Since the medium will slow down the speed of light, the refractive index n one 、 n two Both are greater than 1.
As shown in the right figure Q To point P The propagation time of is

According to Fermat's principle, the path of light propagation is the path where the required time is the extreme value, and the propagation time is taken as T To variable x And set it to zero. After sorting, d can be obtained T /dx＝sin θ one / v one －sin θ two / v two ＝0。
Substitute the relation between propagation speed and refractive index to get the refractive law: n one sin θ one = n two sin θ two 。^[2]

Deduction with Maxwell's electromagnetic field theory

Because light waves are in a specific frequency band electromagnetic radiation Therefore, the light must meet Maxwell's equations Concomitant boundary condition 。 One of the boundary conditions is that the component of electric field parallel to the boundary must have Continuity 。 Assume the boundary is xOy Plane, then at the boundary, there is

E ∥，i ( x ， y ，0)+ E ∥，r ( x ， y ，0)= E ∥，t ( x ， y ，0)。

Among them, E ∥，i 、 E ∥，r 、 E ∥，t They are the components of the electric field of the incident wave, reflected wave and refracted wave (transmission wave) parallel to the boundary.

Assume that the incident wave has a frequency of ω In order to meet the boundary conditions at any time, the frequency of reflected and refracted waves must be ω 。

set up E ∥，i 、 E ∥，r 、 E ∥，t In the form of

E ∥，i = E ∥，i0 exp(i k i · r - ωt )，

E ∥，r = E ∥，r0 exp(i k r · r - ωt )，

E ∥，t = E ∥，t0 exp(i k t · r - ωt )。

Among them, k i 、 k r 、 k t Are the wave vectors of incident wave, reflected wave and refracted wave, E ∥，0 、 E ∥，r0 、 E ∥，t0 The amplitude of incident wave, reflected wave and refracted wave (possibly complex value).

To be anywhere on the boundary（ x ， y , 0) meet boundary conditions, phase The changes must be the same and must be set

k i x x + k i y y = k r x x + k r y y = k t x x + k t y y 。

Therefore, k i x = k r x = k t x ， k i y = k r y = k t y 。

Without losing generality, assumption k i y = k r y = k t y = zero , it can be immediately inferred that the first law is true, and the wave vectors of the incident wave, reflected wave and refracted wave are contained in the incident plane together with the normal of the interface.

Slave wave vector x The equation of component can be obtained

k i sin θ i = k r sin θ r 。

In the same medium, there are k i = k r ，

So, the second law holds, the angle of incidence θ i Equal to reflection angle θ r 。

The definition formula of applied refractive index: n = c / v = ck / ω ，

It can be inferred that the third law holds: n i sin θ i = n t sin θ t 。

Among them, n t 、 θ t They are the refractive index and refractive angle of the refractive medium.

From the phase The three basic laws of geometrical optics can be deduced from the relation.

Generally speaking, for the same beam of light, θ 2 In air ＞ θ 2 In glass ＞ θ 2 Water 。

Novice on the road

Growth task Getting Started with Editing Edit Rule Edit by myself

I have questions

Content query Online Service Official post bar Feedback

Complaints and suggestions

Report bad information Failed to appeal through entries Complaint of infringement information Blocking query and unblocking

Jinggong Network Anbei No. 1100000200001