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Chapter 7

Chapter 7. Ray (Geometric) Optics. Geometry ( 几何学 ) ， Optics ( 光学 ); Reflection ( 反射 ), refraction ( 折射 ); penetrate ( 穿透 ) Ultraviolet ( 紫外线 ); infrared ( 红外线 ), incident ray ( 入射线 ), reflected ray ( 反射线 ) ， refracted ray ( 折射线 ) ， paraxial ray ( 近轴光线 )

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Chapter 7

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  1. Chapter 7 Ray (Geometric) Optics

  2. Geometry (几何学)，Optics (光学); • Reflection (反射), refraction (折射); penetrate (穿透) • Ultraviolet (紫外线); infrared (红外线), • incident ray (入射线), reflected ray (反射线)， refracted ray (折射线)， paraxial ray (近轴光线) • dielectrics (电介质), medium(media,介质), • Spectrum (光谱)， refractive index (折射率) , • fibrescope (纤镜), fiber (光纤) , • interface (界面), focus (焦距，聚焦）， focal distance • dioptric strength (光焦度)，diopter (屈光度)

  3. violet blue green yellow orange red infrared ultraviolet 红外线 紫外线 760 nm 380 nm Wavelength of visible light We know that visible light occupies only a tiny portion in the vast electromagnetic spectrum. Of course, it is a very important part of the spectrum for human beings, since we detect visible radiation with our eyes. Moreover, we distinguish the various visible wavelengths and frequency by their different colors.

  4. Light is able to propagate through certain materials. It can not pass through any metal, but it can penetrate (穿透) some dielectrics (电介质). When light travel in a transparent medium such as air or glass, the velocity is always lower than that in the free space. The ratio of the free space velocity to the velocity in a medium is called refractive index (折射率) of the medium. Velocity of light in the free space Velocity of light in a medium The refractive index depends on the medium in question and on the wavelength of the light. (velocity = f )

  5. 7.1 Reflection and Refraction • Lights can change their propagating direction at the border of a medium or on the boundary between two media. Let’s see what kind of rules they should obey. • Laws of reflection and refraction

  6. Medium #1 Refractive index n1 (1) The incident rays (入射线) (2) reflected ray (反射线) (3) refracted ray (折射线) (4) Three angles Reflected ray Incident ray 3 1 2 Medium #2 Refractive index n2 incident angle, reflective angle, and refractive angle

  7. Law of reflection: Angle of incident = Angle of reflection Law of refraction: n1 is the refractive index of medium 1 and n2 is that of medium 2.

  8. ∴ n1 > n2 2. Total internal reflection (全反射) When light is incident on an interface (界面) from the optically denser medium, it might cause total internal reflection. At the certain critical angle of incidence, all of the incident light is reflected and there are no refraction lights. This phenomenon is called total internal reflection. The critical angle can be easily calculated as the refractive angle in this case is 90 degree.

  9. This phenomenon is widely used in modern technology. For example, light pipe. Light is introduced into one end of a thin glass fiber (光纤) that does not have any sharp bends. As the light progresses, it strikes the walls of the fiber at the incident angles that always exceed the critical angle on the glass-air interface. It causes the light to follow the pipe of the fiber just as the electrical current follows the wire in a circuit. The fiber pipe is widely used in our daily life ranging from decorative displays to telephone cables and also in medical treatment like fibrescope (纤镜).

  10. 7.2 Refraction of a spherical surface and coaxial spherical system 1. Refraction of a spherical surface When the boundary (边界) of two media (介质) is a spherical surface, light refraction is called refraction of a spherical surface(球面折射). The theory of such a refraction is essential and very important for us to understand the light phenomenon of eyes and some other optical systems.

  11. M A n1 n2 i1 h i2     u r Object distance v Image distance We consider the paraxial rays (近轴光线) only which agree with Law of reflection gives and From the figure we know: ∴

  12. M A n1 n2 i1 h i2     u r Object distance v Image distance Considering the paraxial rays, we have

  13. Substituting the relation into We have: (7.1) This is the equation of single spherical surface. It can be applied to all kinds of spherical surface, such as transparent and reflected surfaces, concave, convex surfaces.

  14. Attention: (1). Object distance (物距) u If the direction from object to spherical surface is the same as the direction of light, the object distance u is positive. Otherwise it is negative. (实物物距为正,虚物物距为负) (2). Image distance v If the direction from spherical surface to image is the same as the direction of light, the image distance is positive. Otherwise it is negative. (实像像距为正,虚像像距为负).

  15. (3). Curvature radius r If the direction from spherical surface to its center point is the same as the direction of light, the curvature radius is positive. Otherwise it is negative.

  16. F2 f2 2. Definition of focus When the object (物体) distance is infinity, the image (像) distance is called focal distance and the image point is calledfocus.

  17. The focus of refractive surface. F1 · The first focus of the refractive surface. f1 The first focal distance At this situation, u = f1, v→∞ ∴ ∵ ∴ The first focal distance is

  18. F2 f2 The second focus of the refractive surface n1 Axis of the system n2 In this case, u → ∞, v = f2 ∵ ∴ The second focal distance is ∴

  19. It is found that f1 and f2 are generally different. But the relation between them is related to the refractive indices (折射率) of the two medium. It is easy to find that The ratio of the refractive index to the focal distance in the medium is called dioptric strength (光焦度) of the spherical surface, denoted by D, which is a measure of its ability to cause a beam to converge. With units of diopter (屈光度).

  20. Example 7-1 One end of a cylindrical glass rod is ground (磨) to a hemi-spherical surface of radius R = 20 mm. (1) When the rod is in air, find the image distance of a point object on the axis of the rod, 80 mm to the left of the convex; (2) when the rod is immerged in water of index 1.33, find the image distance. Solution (1) when the rod is in air, n1 = 1.0, n2 = 1.5, r = 20mm, u = 80 mm. Substituting these known conditions into the equation of single spherical surface, we have:

  21. The image is therefore formed at the right of the vertex and at a distance of 120mm from it. (2) Now n1 = 1.33, we have The fact that v is negative means that the rays, after refraction by the surface, are not converging but appear to diverge from a point 180mm to the left of vertex. This kind of image is called virtual image.

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