Lecture 11 Reflection & Refraction

Instructor: Kazumi Tolich Lecture 11

¨ Reading chapter 31-3 ¤ Reflection ¤ Refraction ¤ Dispersion Reflection and refraction

¨ The angle between the incident ray and the normal is called the angle of incidence.

¨ The plane containing the incident ray and the normal is called the plane of incidence.

¨ When a beam of light strikes a boundary surface, part of the light energy is reflected at an angle given by the law of reflection: � = � ¨ If the angle of incidence is not zero, the transmitted beam is bent, or refracted.

Incident light Reflected ray

Refracted ray Demo 1

¨ Angle of Incidence and Reflection ¤ Demonstration of angles of incidence and reflection Snell’s law

¨ The angle of transmitted ray, θ2, is called angle of refraction. ¨ The angles of incidence and refraction, and indices of refraction of two media are related by Snell’s Law: � sin � = � sin � ¤ In a medium in which light slows down, a ray bends closer to the normal. Demo 2

¨ Refraction and Reflection from Plastic Block ¤ Demonstration of Snell’s law: the ray bends closer to the normal in the plastic.

¤ � sin � = � sin � Quiz: 1 Quiz: 11-1 answer

¨ You are trying to catch fish by using a spear. You observe a large fish a couple of meters in front of you and a meter below the water surface. Assuming that the fish is stationary, in order to hit the fish with your spear you must aim slightly below the point where you see the fish. ¨ For you to see the fish, the light must travel from the fish to your eyes. ¨ The ray is refracted at the water-air boundary. ¨ The angle of incidence is smaller than the angle of refraction since light travels faster in air than in water. Example 1

¨ A 2.00 m long vertical pole extends from the bottom of a swimming pool to a point 50.0 cm above the water. Sunlight is incident at 55.0º above the horizon. What is the length of the shadow of the pole on the level bottom of the pool? The indices of refraction of air and water are 1.00 and 1.33, respectively. Specular reflection

¨ Reflection from a smooth surface is called specular reflection.

¨ After reflection, the rays diverge exactly as if they came from a point P’ called the image point. Demo 3

¨ Location of Image (candle in glass of water) ¤ Demonstration of image point. Diffuse reflection

¨ When light reflects off a rough surface, diffuse reflection, the rays from a point reflect in random directions and do not diverge from any point, failing to form any image. ¨ Light reflected off a dry street is a diffuse reflection, but light reflected off a wet street becomes more specular, and it makes difficult to see what is on the road. Demo 4

¨ Diffuse/Specular Reflection ¤ Comparison of diffuse reflection off a rough surface and specular reflection. Intensities of reflected light

¨ The fraction of light energy reflected at a boundary depends on the angle of incidence, the orientation of the E field (polarization), and the indices of refraction of the two media. ¨ For the special case of normal incidence

(θ1 = θ’1 = 0), the reflected intensity is given by

n2 Example 2

¨ 16 % of light energy is reflected from an air-diamond interface at normal incidence. How fast does light travel in diamond? Total internal reflection

¨ When the incident light is in a medium with a higher index of refraction, the angle of refraction is greater than the incident angle.

¨ For incident angles greater than the critical angle, and no refracted ray exists. This phenomenon is called total internal reflection. The critical angle,

θc, is given by � n � = sin 2 �

n1 Binoculars

¨ If the index of refraction of the glass is typical 1.5, the critical angle for total internal reflection is 41.8º.

¨ If the angle of incidence of the ray on the glass–air interface is 45º, the light will be totally reflected.

¨ In binoculars, two prisms are used on each side.

Glass prism Fiber optics

¨ Total internal reflection in fiber optic light pipes makes it possible to transport light and light-encoded signals over long distances without significant loss. Demo 5

¨ Critical Angle and Total Internal Reflection

¨ Light Pipes and Fiber Optics FlipItPhysics-8: Swimming Pool

¨ Can the person standing on the edge of the pool be prevented from seeing the light by total internal reflection at the water-air surface?

¨ No! The ray that makes smaller incident angle still makes out of water. Example 3

¨ A light bulb is set in the bottom of a 3.0 m deep swimming pool. What is the diameter of the pool’s surface where the light can escape?

h = 3.0 m Mirages

¨ The speed of light wave is slightly greater in the less dense layer of hot air near the pavement, so a light beam passing from the cooler layer into the warmer layer is bent.

Uniform temperature Hot near the ground Dispersion and n(λ)

¨ The index of refraction of a transparent material varies as a function of λ. ¨ White light entering a prism is separated into different colors (dispersion). Rainbows

¨ The separation of the colors in the rainbow results from dispersion of the sunlight in raindrops.

¨ The color seen at a particular angle corresponds to the wavelength of light that allows the light to reach the eye from the droplets at that angle.

Sunlight Raindrops

Observer Quiz: 2 Quiz 11-2 answer

¨ Which of the following statements is true about the speeds of the various colors of light in glass? ¨ Red has the highest speed, violet the lowest. ¨ The red light bends least, so the speed of red light is closest to the speed of light in air. Quiz: 3 Quiz 11-3 answer

¨ Of the following quantities, the one that is independent of the frequency of light is the angle of reflection. (� = �) ¨ Polarization angle (tan� = ), critical angle (� = sin ), and refraction angle (� sin � = � sin �) depend on indices of refraction, which depend on the wavelength of the light.