Chapter 35

1. Chapter 35 The Laws of Geometric Optics

2. The Ray Approximation of Light in Geometric Optics • Geometric optics studies the propagation of light. • Light travels in a straight-line path in a uniform medium. Light changes its direction when it meets the interface of two media. Here reflection and refraction take place. • Propagation of light in non-uniform medium is not discussed here. • The ray approximation is used to represent beams of light. Each ray is represented as a line. The rays are straight lines perpendicular to the wave fronts • The path of light is reversible.

3. Reflection of Light Specular reflection • Reflection: a ray of light, the incident ray, changes its direction at the interface of two media, and travels back in the same medium of the incident ray. • Two types of reflection: • Specular reflection: reflection from a smooth surface. For parallel incidence, the reflected rays are parallel to each other. • Diffuse reflection: reflection from a rough surface. Reflected rays travel in a variety of directions even for parallel incidence. • We will only discuss specular reflections here. Medium 1 Medium 2 Diffuse reflection Medium 1 Medium 2

4. Law of Reflection • The incident angle and the reflection angle. • Incident angle: the angle ( in the diagram) the incident ray makes with the normal of the interface at which the reflection takes place. • Reflection angle: the angle ( in the diagram) the reflected ray makes with the normal of the interface at which the reflection takes place. • The Law of reflection: The incident ray, the reflected ray and the normal are all in one plane.

5. Retroreflection • Retroreflection: reflected light travels in parallel but opposite in direction to the incident light. • Can be achieved by two plane mirrors with an angle of 90o between them. • Applications include • Measuring the distance to the Moon • Automobile taillights • Traffic signs

6. One more example problem The distance of a lightbulb from a large plane mirror is twice the distance of a person from the same mirror. Light from the lightbulb reaches the person by two paths. It travels to the mirror at an angle of incidence θand reflects from the mirror to the person. It also travels directly to the person without reflecting off the mirror. The total distance traveled by the light in the first case is twice the distance traveled by the light in the second case. Find the angle θ.

7. Refraction of Light • Refraction: When light enters from one medium to the second, it changes its direction in the second medium. The angle the refracted light makes with the normal ( in the diagram) is called the angle of refraction. • The incident ray, the reflected ray, the refracted ray, and the normal all lie in the same plane. • The reason for this bend is because light travels at different speeds in different medium: Here is the speed of light in medium 1, is the speed of light in medium 2. Medium 1 Medium 2

8. Snell’s Law of Refraction • The index of refraction: • Because the speed of light in any material is less than its speed in vacuum, index of refraction • For a vacuum, n= 1 • For air n = 1 is a very good approximation. • For other media, n > 1 • Snell’s Law of refraction

9. Reflection and Refraction

10. Some Indices of Refraction

11. Frequency Between Media • When light travels from one medium to another, its frequency does not change (this comes from energy conservation) • Both the speed and the wavelength do change From: One has: Index of refraction is a function of frequency (color). Different colors of light bent differently when refracted.

12. Variation of Index of Refraction with Wavelength • The index of refraction for a material generally decreases with increasing wavelength • Violet light bends more than red light when passing into a refracting material

13. Dispersion • For a given material, the index of refraction varies with the wavelength or frequency of the light passing through the material • This dependence of n on is called dispersion • So by Snell’s, light of different wavelengths is bent at different angles when incident on a refracting material

14. Prism • A ray of single-wavelength light incident on the prism will emerge at angle d from its original direction of travel • dis called the angle of deviation • F is the apex angle • The angle d can be expressed as a function of the incident angle, the apex angle, and refractive index. • When a ray of white light (many colors) enters a prism, the color components are separated out into a spectrum: • Violet deviates the most • Red deviates the least • The remaining colors are in between.

15. The Rainbow, Nature’s show of dispersion • Sun light refracted/reflected by rain drops has its color components separated into color spectrum. • The angle between the white light and the most intense violet ray is 40° • The angle between the white light and the most intense red ray is 42°

16. Double Rainbow • The secondary rainbow is fainter than the primary • The colors are reversed • The secondary rainbow arises from light that makes two reflections from the interior surface before exiting the raindrop • Higher-order rainbows are possible, but their intensity is low

17. Total Internal Reflection • When light travels from a medium with larger index of refraction to a medium with smaller n, as in the diagram n1 > n2. The refracted angle is larger than the incident angle. • As the incident angle increases to the point that the refracted angle is 90o, this incident angle is called the critical angle θc. Beyond it, there is no refraction. All light is reflected back and this phenomenon called total internal reflection. From Snell’s Law: When medium 2 is air:

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

19. 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

20. 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

21. Fiber optics What is the maximum angle α that results in total internal reflection inside the fiber optic cable? This angle is usually called the launching angle in fiber optics.