Image Formation by Refraction

Transcription

1 Image Formation by Refraction If you see a fish that appears to be swimming close to the front window of the aquarium, but then look through the side of the aquarium, you ll find that the fish is actually farther from the window than you thought Pearson Education, Inc. Slide 34-1

2 Image Formation by Refraction Rays emerge from a material with n 1 n 2. Consider only paraxial rays, for which θ 1 and θ 2 are quite small. In this case: where s is the object distance and s is the image distance Pearson Education, Inc. Slide 34-2

3 QuickCheck A fish in an aquarium with flat sides looks out at a hungry cat. To the fish, the distance to the cat appears to be A. Less than the actual distance. B. Equal to the actual distance. C. More than the actual distance Pearson Education, Inc. Slide 34-3

4 Example 1 A fish and a sailor look at each other through a 5.0-cm-thick glass porthole in a submarine. There happens to be an air bubble right in the center of the glass. How far behind the surface of the glass does the air bubble appear to the fish? To the sailor? 2017 Pearson Education, Inc. Slide 34-4

5 Total Internal Reflection When a ray crosses a boundary into a material with a lower index of refraction, it bends away from the normal. As the angle θ 1 increases, the refraction angle θ 2 approaches 90º, and the fraction of the light energy transmitted decreases while the fraction reflected increases. The critical angle of incidence occurs when θ 2 = 90º: The refracted light vanishes at the critical angle and the reflection becomes 100% for any angle θ 1 > θ c Pearson Education, Inc. Slide 34-5

6 Total Internal Reflection 2017 Pearson Education, Inc. Slide 34-6

7 QuickCheck Light passes from a medium of index of refraction n a into a second medium of index of refraction n b. The critical angle for total internal reflection is In order for total internal reflection to occur, what must be true about n a, n b, and the incident angle? 2016 Pearson Education, Inc.

8 QuickCheck A periscope can be used to provide a view of an otherwise obstructed field. Which of the following diagrams illustrates the correct arrangement of prisms in a simple periscope? A B C D 2016 Pearson Education, Inc.

9 QuickCheck A laser beam undergoes two refractions plus total internal reflection at the interface between medium 2 and medium 3. Which is true? A. n 1 < n 3 B. n 1 > n 3 C. There s not enough information to compare n 1 and n Pearson Education, Inc. Slide 34-9

10 Example 2 A small lightbulb is set in the bottom of a 3.0-m-deep swimming pool. What is the diameter of the circle of light seen on the water s surface from above? 2017 Pearson Education, Inc. Slide 34-10

11 In-class Activity 1 Light enters a solid tube made of plastic having an index of refraction of You want to cut the face AB so that all the light will reflect back into the tube after it first strikes that face. (a) What is the largest that θ can be if the pipe is in air? (b) If the pipe is in water (n = 1.33), what is the largest that θ can be? 2016 Pearson Education, Inc.

12 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 Pearson Education, Inc. Slide 34-12

13 Fiber Optics In a practical optical fiber, a small-diameter glass core is surrounded by a layer of glass cladding. The glasses used for the core and the cladding have n core n cladding 2017 Pearson Education, Inc. Slide 34-13

14 Dispersion The speed of light in vacuum is the same for all wavelengths, but the speed in a material substance is different for different wavelengths. The dependence of wave speed and index of refraction on wavelength is called dispersion. In most materials the value of n decreases with increasing wavelength and decreasing frequency Pearson Education Inc.

15 Dispersion Ordinary white light is a superposition of waves with all visible wavelengths. The band of dispersed colors is called a spectrum Pearson Education Inc.

16 Example 3 The indices of refraction for violet light (λ = 400 nm) and red light (λ = 700 nm) in diamond are 2.46 and 2.41, respectively. A ray of light traveling through air strikes the diamond surface at an angle of 51.5º to the normal. Calculate the angular separation between these two colors of light in the refracted ray.

17 How rainbows form: Slide 1 of 3 When sunlight enters a spherical water droplet suspended in the air, it is (partially) reflected from the back surface of the droplet, and is refracted again upon exiting the droplet. A light ray that enters the middle of the raindrop is reflected straight back. All other rays exit the raindrop within an angle Δ of that middle ray, with many rays piling up at the angle Δ Pearson Education Inc.

18 How rainbows form: Slide 2 of Pearson Education Inc.

19 How rainbows form: Slide 3 of 3 In many cases you can see a second, larger rainbow. It is the result of two reflections from the back surface of the droplet. Just as a mirror held up to a book reverses the printed letters, so the second reflection reverses the sequence of colors in the secondary rainbow Pearson Education Inc.

20 Huygens s principle Huygens s principle states that every point of a wave front may be considered the source of secondary wavelets that spread out in all directions with a speed equal to the speed of propagation of the wave. The new wave front at a later time is then found by constructing a surface tangent to the secondary wavelets or, as it is called, the envelope of the wavelets. The figure shows the application of Huygens s principle to wave front to construct a new wave front 2016 Pearson Education Inc.

21 Huygens Principle: Plane Waves 2017 Pearson Education, Inc. Slide 32-21

22 Reflection and Huygens s principle To derive the law of reflection from Huygens s principle, we consider a plane wave approaching a plane reflecting surface. The effect of the reflecting surface is to change the direction of travel of those wavelets that strike it. The angle θ a therefore equals the angle θ r, and we have the law of reflection Pearson Education Inc.

23 Refraction and Huygens s principle Huygens s principle can be used to explain the law of refraction Pearson Education Inc.

24 A mirage Mirages are an example of Huygens s principle. A thirsty traveler can interpret the apparent reflecting surface as a sheet of water Pearson Education Inc.

25 Polarization An electromagnetic wave is linearly polarized if the electric field has only one component. Light from most sources such as light bulbs is a random mixture of waves linearly polarized in all possible transverse directions; such light is called unpolarized light or natural light. A Polaroid polarizing filter can convert unpolarized light to linearly polarized light Pearson Education Inc.

26 Malus s law When polarized light of intensity I max is incident on a polarizing filter used as an analyzer, the intensity I of the light transmitted through the analyzer depends on the angle ϕ between the polarization direction of the incident light and the polarizing axis of the analyzer Pearson Education Inc.

27 QuickCheck Three polarizing filters are stacked with the polarizing axes of the second and third filters oriented at 45º and 90º, respectively, relative to the polarizing axis of the first filter. Unpolarized light of intensity I 0 is incident on the first filter. The intensity of light emerging from the third filter is 2016 Pearson Education, Inc.

28 Example 4 Unpolarized light of intensity I o passes through two polarizers as seen in the figure. Find the intensity of light picked up by the photocell if the angle between the axes of the two filters is 30º.

29 Polarization by reflection Unpolarized light can be polarized, either partially or totally, by reflection. At one particular angle of incidence, called the polarizing angle, the light for which lies in the plane of incidence is not reflected at all but is completely refracted Pearson Education Inc.

30 Example 5 A parallel beam of unpolarized light in air is incident at an angle of 57.5º on a plane glass surface. The reflected beam is completely linearly polarized. (a) What is the index of refraction of the glass? (b) What is the angle of refraction of the transmitted beam?