1. Chapter 35 The Nature of Light and the Laws of Geometric Optics

2. 피조의 톱니바퀴를 이용한 빛의 속력 측정예제 35.1 360 개의 톱니를 가진 피조의 톱니바퀴가 27.5 회 / 초로 회전하고 있다. 그림 35.2 에서 톱니의 홈 A 를 통과한 빛이 반사되어 돌아올 때, 톱니 B 에 의하여 막히게 된다. 거울까지의 거리가 7500 m 일 때, 빛의 속력을 구하라. 풀이 톱니바퀴의 홈은 360 개. 빛이 거울까지 왕복 운동하는 동안 톱니바퀴는 1/720 회 회전. 35.3 기하 광학에서의 광선 근사 (The Ray Approximation in Geometric Optics) 35.3 기하 광학에서의 광선 근사 (The Ray Approximation in Geometric Optics) 기하 광학 (geometric optics) 기하 광학 (geometric optics) : 빛은 균일한 매질을 지날 때에는 직선 방향으로 고정된 방향으로 진행하고, 다른 매질과의 경계면을 만나거나, 시간적으로 또는 공간에 따라 매질의 광학적 성질이 불균일할 때에는 진행 방향을 바꾼다고 가정. 광선 근사 (ray approximation) 광선 근사 (ray approximation) : 광선이란 평면파의 경우 파면에 수직인 직선. 광선 근사에서, 매질을 통하여 이동하는 파동은 광선의 방향을 따라 직선으로 진행한다.

3. The Ray Approximation in Geometric Optics Geometric optics involves the study of the propagation of light It uses the assumption that light travels in a straight-line path in a uniform medium and changes its direction when it meets the surface of a different medium or if the optical properties of the medium are nonuniform The ray approximation is used to represent beams of light

4. Ray Approximation The rays are straight lines perpendicular to the wave fronts With the ray approximation, we assume that a wave moving through a medium travels in a straight line in the direction of its rays

5. Ray Approximation, cont. If a wave meets a barrier, we will assume that λ<<d d is the diameter of the opening This approximation is good for the study of mirrors, lenses, prisms, etc. Other effects occur for openings of other sizes

6. Law of Reflection The normal is a line perpendicular to the surface It is at the point where the incident ray strikes the surface The incident ray makes an angle of θ 1 with the normal The reflected ray makes an angle of θ 1 ’ with the normal

7. Law of Reflection, cont. The angle of reflection is equal to the angle of incidence θ 1 ’= θ 1 This relationship is called the Law of Reflection The incident ray, the reflected ray and the normal are all in the same plane Because this situation happens often, an analysis model, wave under reflection, is identified

8. Retroreflection Assume the angle between two mirrors is 90 o The reflected beam returns to the source parallel to its original path This phenomenon is called retroreflection Applications include Measuring the distance to the Moon Automobile taillights Traffic signs

9. 이중으로 반사된 광선예제 35.2 그림과 같이 두 개의 거울이 서로 120° 의 각을 이루고 놓여있다. 거울 M 1 에 65° 의 입사각으로 들어온 광선이 거울 M 2 로부터 반사될 때의 방향을 구하라. 풀이 첫 번째 반사 광선이 수평면과 이루는 각도 그림에서 입사 광선과 반사 광선을 거울 뒤로 연장하면 두 광선은 60° 의 각으로 교차할 것이며, 광선의 방향 변화는 모두 120° 가 된다. 이는 곧 거울의 사이각이다. 광선의 방향 변화는 항상 거울의 사이각과 일치하지는 않으며, 위의 경우는 특별한 경우이다. 사이각이 90 도인 경우 방향 변화는 180 도가 되어 반사된 빛은 원래의 방향으로 돌아가게 된다.

10. Refraction of Light When a ray of light traveling through a transparent medium encounters a boundary leading into another transparent medium, part of the energy is reflected and part enters the second medium The ray that enters the second medium is bent at the boundary This bending of the ray is called refraction

11. Refraction, 2 The incident ray, the reflected ray, the refracted ray, and the normal all lie on the same plane The angle of refraction depends upon the material and the angle of incidence v 1 is the speed of the light in the first medium and v 2 is its speed in the second

12. Refraction of Light, 3 The path of the light through the refracting surface is reversible For example, a ray that travels from A to B If the ray originated at B, it would follow the line AB to reach point A

13. Following the Reflected and Refracted Rays Ray  is the incident ray Ray  is the reflected ray Ray is refracted into the lucite Ray  is internally reflected in the lucite Ray is refracted as it enters the air from the lucite

14. Light in a Medium The light enters from the left The light may encounter an electron The electron may absorb the light, oscillate, and reradiate the light The absorption and radiation cause the average speed of the light moving through the material to decrease

15. The Index of Refraction The speed of light in any material is less than its speed in vacuum The index of refraction, n, of a medium can be defined as

16. Index of Refraction, cont. For a vacuum, n = 1 We assume n = 1 for air also For other media, n > 1 n is a dimensionless number greater than unity n is not necessarily an integer

17. Some Indices of Refraction

18. Frequency Between Media As light travels from one medium to another, its frequency does not change Both the wave speed and the wavelength do change The wavefronts do not pile up, nor are created or destroyed at the boundary, so ƒ must stay the same 물 공기 ƒ 1 = ƒ 2

19. Index of Refraction Extended The frequency stays the same as the wave travels from one medium to the other v = ƒλ ƒ 1 = ƒ 2 but v 1  v 2 so λ 1  λ 2 The ratio of the indices of refraction of the two media can be expressed as various ratios

20. More About Index of Refraction The previous relationship can be simplified to compare wavelengths and indices: λ 1 n 1 = λ 2 n 2 In air, n 1 = 1 and the index of refraction of the material can be defined in terms of the wavelengths

21. Snell’s Law – Example Light is refracted into a crown glass slab θ 1 = 30.0 o, θ 2 = ? n 1 = 1.00 and n 2 = 1.52 From Table 35.1 θ 2 = sin -1 (n 1 / n 2 ) sin θ 1 = 19.2 o The ray bends toward the normal, as expected 실제 깊이 허상

22. 유리의 굴절각예제 35.3 파장이 589nm 인 빛이 공기 중에서 투명하고 평평한 크라운 유리로 법선과 이루는 입사각 30.0° 인 상태로 입사한다. (A) 굴절각, (B) 유리에서 이 빛의 속력 및 (C) 빛의 파장을 구하라. 풀이 이므로 (A) 굴절각 ; (B) 속력, 파장 ;

23. 평행판을 투과하는 빛예제 35.4 빛이 매질 1 로부터 매질 2, 즉 굴절률이 n 2 인 두꺼운 평행판을 투과한다. 투과된 빛이 입사한 빛과 평행함을 보여라. 풀이 만약 평행판의 두께가 두 배로 되면 두 광로 사이의 거리 d 도 두 배로 되는가 ? 광로 사이의 거리 d 가 평행판 두께에 비례한다. and

24. Observing the Rainbow If a raindrop high in the sky is observed, the red ray is seen A drop lower in the sky would direct violet light to the observer The other colors of the spectra lie in between the red and the violet

25. Total Internal Reflection A phenomenon called total internal reflection can occur when light is directed from a medium having a given index of refraction toward one having a lower index of refraction

26. Possible Beam Directions Possible directions of the beam are indicated by rays numbered 1 through 5 The refracted rays are bent away from the normal since n 1 > n 2

27. Critical Angle There is a particular angle of incidence that will result in an angle of refraction of 90° This angle of incidence is called the critical angle, θ C

28. 물고기의 눈에 보이는 광경예제 35.6 물의 굴절율이 1.33 이라면, 물과 공기의 경계면에서 임계각은 얼마인가 ? 풀이 이므로 물 속에서 밖을 볼 때, 물 공기 이면 물 속에서 밖을 볼 수 없다.

29. Fiber Optics An application of internal reflection Plastic or glass rods are used to “pipe” light from one place to another Applications include Medical examination of internal organs Telecommunications

30. Fiber Optics, cont. A flexible light pipe is called an optical fiber A bundle of parallel fibers (shown) can be used to construct an optical transmission line

31. Construction of an Optical Fiber The transparent core is surrounded by cladding The cladding has a lower n than the core This allows the light in the core to experience total internal reflection The combination is surrounded by the jacket