1 By Mike Maloney

© 2003 Mike Maloney2 Light as a Ray Light very often travels in straight lines. We represent light using rays, which are straight lines emanating from an object. This is an idealization, but is very useful for geometric optics.

© 2003 Mike Maloney3 Light as a Ray When the source of light is very far away (like the sun) we can assume that the rays are all coming in parallel to each other. In other cases, they radiate out from the source in all direction.

© 2003 Mike Maloney4 Reflection We know that when a wave meets a boundary (change in medium), part of it gets reflected. The same is true for light waves … if they didn’t we wouldn’t really see anything at all. When a light wave meets a boundary with something that is opaque, it is reflected.

© 2003 Mike Maloney5 Reflection Law of reflection: the angle of reflection (that the ray makes with the normal to a surface) equals the angle of incidence.

© 2003 Mike Maloney6 Reflection The law states that the angle that a light ray is reflected is equal to the angle it hits the surface at (aka angle of incidence. Or in laymen's terms, the angle the light leaves the surface at is the same as the angle that it hits the surface at.

© 2003 Mike Maloney7 Reflection If all opaque objects reflect light, how come I can’t see my image in the wall or your shirt, but I can in a mirror? Because all surfaces are not flat, even the ones that look like they are. Regular (Specular) Reflection, is the kind that you see when you look in a mirror. All the light rays reflect parallel to each other, so the reflected image looks the same, just flipped left to right. Diffuse Reflection is what happens when the surface is not flat. The reflected light rays do not end up parallel to each other.

© 2003 Mike Maloney8 Diffuse Reflection When light reflects from a rough surface, the law of reflection still holds, but the angle of incidence varies. This is called diffuse reflection.

© 2003 Mike Maloney9 Diffuse Reflection With diffuse reflection, your eye sees reflected light at all angles. With specular reflection (from a mirror), your eye must be in the correct position. Diffuse Reflection Specular Reflection

© 2003 Mike Maloney10 Perception and Reflection What you see when you look into a plane (flat) mirror is an image, which appears to be behind the mirror.

© 2003 Mike Maloney11 Refraction Have you ever looked at your legs in a pool …or looked at a pencil in a glass of water? You may notice that they seem to bend. This phenomenon is called REFRACTION. Can you guess why it might happen? HINT: remember light is a wave …

© 2003 Mike Maloney12 Refraction When light passes from one medium to another at an angle it seems to bend. This is due to the fact that it slows down or speeds up when it changes mediums. n (index of refraction) is an experimental number used to compare different materials to each other based on how much they slow down light. n = (speed of light in vacuum) / (speed of light in medium) n = c / v = o / n is always bigger than 1. Why is this true?

© 2003 Mike Maloney13 Some indices of Refraction What happens to the wavelength of light when it enters a new medium? BACK

© 2003 Mike Maloney14 Less Dense to More Dense When light travels from a less dense to a more dense medium and does not hit is straight on, it slows down and bends towards the center.

© 2003 Mike Maloney15 More Dense to Less Dense And what do you think happens when you go from more dense to less dense? Right it speeds up and bends away from the middle.

© 2003 Mike Maloney16 Refraction Light changes direction when crossing a boundary from one medium to another. This is called refraction, and the angle the outgoing ray makes with the normal is called the angle of refraction.

© 2003 Mike Maloney17 Refraction Different materials bend light at different amounts n (index of refraction) can also be used to compare different materials to each other based on how much they bend light.

© 2003 Mike Maloney18 Snell’s Law A ray of light bends in such a way that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, and this constant is the index of refraction. OR, n = Sin Θ i Sin Θ r n = index of refraction Θ i = angle of incidence (incoming angle) Θ r = angle of refraction (outgoing/bent angle) ** NOTE this equation is only good when the light is incident in air or a vacuum.

© 2003 Mike Maloney19 Snell’s Law n r / n i = sin Θ i / sin Θ r Or by playing with the math n 1 sinΘ 1 = n 2 sinΘ 2 In this equation n 1 and n 2 are the index of refractions of each material, and Θ 1 and Θ 2 are the corresponding angles. Θ is always measured from the normal line. Let’s try an example.Let’s try an example

© 2003 Mike Maloney20 Why are you short in water? Refraction is what makes objects half-submerged in water look odd.

© 2003 Mike Maloney21 Total Internal Reflection What would happen if when light went from a more dense medium to a less dense medium and the angle of refraction was greater than 90°? n = 1.33 n = 1.0

© 2003 Mike Maloney22 Total Internal Reflection What would happen if when light went from a more dense medium to a less dense medium and the angle of refraction was greater than 90°? You would get something called total internal reflection. The light would be refracted so much that the ray never makes it outside of the medium, and no transmission would occur. The light would all reflect at the same incident angle.

© 2003 Mike Maloney23 Total Internal Reflection As the incident angle increases, the refracted angle gets closer to 90 °. The minimum angle that causes total internal reflection ( Θ r = 90°) between two materials is known as the critical angle (θ c ).

© 2003 Mike Maloney24 Critical Angle Θ C It is found using Snell’s law and setting the angle of refraction to 90° and solving for the angle of incidence. n 1 sinΘ c = n 2 sin(90°) If Θ C is bigger than 90°, no transmission occurs, only reflection.

© 2003 Mike Maloney25 Finding the Critical Angle Θ C Lets find the critical angle for light moving from water to air. n water = 1.33, n air = 1.00 n 1 sinΘ 1 = n 2 sin(90°) 1.33*sinΘ 1 = 1*sin(90) sinΘ 1 = 1/1.33 =.75 Θ 1 = sin -1 (0.75) Θ 1 = 48.6 deg

© 2003 Mike Maloney26 Summary of Equations Reflection Refraction

© 2003 Mike Maloney27 Some Effects Of Refraction Mirages Prisms Rainbows Lenses Fiber-optics

© 2003 Mike Maloney28 Mirages The high temperature near the ground changes the index of refraction of the air near the ground. This makes the light curve or refract. If it is hot enough, the light coming down can curve back up into your eyes and you see a “fake” reflection.

© 2003 Mike Maloney29 Prisms Different wavelengths of light have slightly different indices of refraction. When white light moves through a prism all the colors get refracted twice, each by a slightly different amount. When they emerge they are no longer on top of each other, but are now separated (dispersed).

© 2003 Mike Maloney30 Rainbows

© 2003 Mike Maloney31 Rainbows Explained Different colors of light get diffracted different amounts when they travel through water. This causes a spectrum of light to appear in the sky when the Sun shines onto droplets of moisture in the Earth's atmosphere. White light enters and refracts, reflects off the back and refracts again as it comes out. The various colors have been refracted different amounts and are no longer on top of each other. What you see is a pattern of different refracted colors from different drops (red from one drop, green from another, blue from another) in the shape of a bow that reach your eyes. Everyone sees a different rainbow.

© 2003 Mike Maloney32 Lenses A lens can be used to focus light. Depending on where on the lens the light hits, it has different incoming angle, and therefore leaves at a different refracted angle. If the lens is shaped right, all the waves focus on a point called the focal point. What is the purpose of your eyeglasses?

© 2003 Mike Maloney33 Fiber Optics/TV Rock Light will be transmitted along the fiber even if it is not straight. An image can be formed using multiple small fibers.