Ray Optics. Lecture 23. Chapter 23. Physics II. Course website:

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1 Lecture 23 Chapter 23 Physics II Ray Optics Course website:

2 Let s finish talking about a diffraction grating

3 Diffraction Grating Let s improve (more convenient to use) results of a double-slit system. How? Spacing between bright spots: Δ We saw in the demo that the spacing between bright spots is inconveniently small ( mm), but we can increase the spacing by reducing d Intensity of bright spots: 2 cos Number of slits We saw in the demo that the intensity of the bright spots is not bright enough, but we can increase brightness by increasing number of slits (N) Thus, we can replace the double slit with an opaque screen that has N closely spaced slits. A large number of equally spaced parallel slits is called a diffraction grating.

4 The Diffraction Grating The figure shows a diffraction grating in which N slits are equally spaced a distance d apart. When illuminated from one side, each of these slits becomes the source of a light wave that diffracts, or spreads out, behind the slit. A practical grating will have hundreds or even thousands of slits. Physics and math are the same as for a double-slit experiment sin, Bright fringes will occur at angles m., It s easier to measure distances 0,1,2, on the screen than angles: θ y However, these angles are NOT SMALL AND the equations CANNOT BE SIMPLIFIED like we did for the 2slit experiment. Thus, using these two equations we can find positions of the bright spots. The integer m is called the order of the diffraction.

5 Diffraction grating intensity Now with N slits, the wave amplitude at the points of constructive interference is Na. Because intensity depends on the square of the amplitude, the intensities of the bright fringes are: Not only do the fringes get brighter as N increases, they also get narrower. The bright spots are no longer equally spaced.

6 Measuring wavelength emitted by a diode laser (with a demonstration) Light from a diode laser passes through a diffraction grating having 300 slits per millimeter. The interference pattern is viewed on a wall 2.5 m behind the grating. Calculate the wavelength of the laser.

7 Ray Optics

8 Ray Optics Wave Optics (object size) Ray Optics (object size)

9 The Ray Model of Light Ray Ray Let us define a light ray as a line in the direction along which light energy is flowing. Ray Ray Wave fronts Now, we will model light with rays, straight lines to wave fronts. This model is valid as long as an object is very large compared to the wavelength. Any narrow beam of light, such as a laser beam, is actually a bundle of many parallel light rays.

10 Types of objects Self-luminous object (active) It emits light Ray Reflective object (passive) It reflects light Objects can be either self-luminous, such as the sun, flames, and lightbulbs, or reflective. Most objects are reflective.

11 How Rays interact with media Light interacts with matter in four different ways: At an interface between two materials, light can be either reflected or refracted. Within a material, light can be either scattered or absorbed. Medium 1 Medium 2 Reflection Refraction

12 Reflection

13 Two types of reflections Specular Reflection (from a smooth surface) Incident ray Reflected ray Diffuse Reflection (from a rough surface) Incident ray Reflected angle of incidence angle of reflection Law of reflection: 1. Incident and reflected rays and a normal line are in the same plane 2. Angle of incident equals to angle of reflection For a rough surface, the law of reflection is obeyed at each point but the irregularities of the surface cause the reflected rays to leave in many random directions. Most objects are seen by virtue of their reflected light. It is how you see this slide, the wall, your hand, your friend, and so on.

14 Image in a plane mirror I Consider P, a source of rays which reflect from a mirror. The reflected rays appear to emanate from P, the same distance behind the mirror as P is in front of the mirror. That is, s = s. mirror s s Cat vs Mirror

15 Image in a plane mirror II

16 ConcepTest Two point sources of light illuminate a narrow vertical aperture in a dark screen. What do you see on the viewing screen? Ray Optics screen

17 Refraction

18 Refraction Two things happen when a light ray is incident on a smooth boundary between two transparent materials: 1. Part of the light reflects from the boundary, obeying the law of reflection. 2. Part of the light continues into the second medium. The transmission of light from one medium to another, but with a change in direction, is called refraction. Refracted ray

19 Indices of Refraction The index of refraction is used to describe optical properties of a transparent medium. Speed of light in a medium

20 Refraction Consider a smooth boundary between two transparent materials Incident ray angle of incidence Normal Reflected ray The ray has a kink at the boundary Medium 1 Medium 2 Assume n 2 > n 1 angle of refraction Refracted ray

21 When a ray is transmitted into a material with a higher index of refraction, it bends toward the normal. Refraction When a ray is transmitted into a material with a lower index of refraction, it bends away from the normal. n 2 > n 1 n 2 < n 1 It bends toward the normal It bends away from the normal

22 ConcepTest Refraction A laser beam passing from medium 1 to medium 2 is refracted as shown. Which is true? A. n 1 < n 2. B. n 1 > n 2. C. There s not enough information to compare n 1 and n 2. n 2 < n 1 It bends away from the normal The end of the class

23 Total internal reflection

24 n 2 < n 1 angle of incidence Total Internal Reflection Normal angle of refraction Refracted ray air =900 n glass 1 < Incident ray Reflected ray When a ray crosses a boundary into a material with a lower index of refraction, it bends away from the normal. As the angle 1 increases, the refraction angle 2 approaches 90, and the fraction of the light energy transmitted decreases while the fraction reflected increases. The critical angle of incidence occurs when 2 = 90 : The refracted light vanishes at the critical angle and the reflection becomes 100% for any angle 1 > c.

25 Critical angle (TIR) n 2 < n 1 n 1 Normal angle of refraction air =90 0 glass Refracted ray =90 0 Critical angle (incident angle) Angle of refraction, so 1 sin sin 90 Total Internal Reflection Critical angle sin

26 Fiber Optics The most important modern application of total internal reflection (TIR) is optical fibers. Light rays enter the glass fiber, then impinge on the inside wall of the glass at an angle above the critical angle, so they undergo TIR and remain inside the glass. The light continues to bounce its way down the tube as if it were inside a pipe.

27

28 What you should read Chapter 23 (Knight) Sections

29 Thank you See you on Tuesday

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