Lecture 15 Reflection & Refraction

18.1 The ray model of light Endoscopes use fiber optics. Source of light rays Ray diagrams Seeing objects Shadows 18.2 Reflection Diffuse reflection The plane mirror 18.3 Refraction Examples of refraction Total internal reflection Fiber optics 18.1 The ray model of light

! A light ray is a line in the direction along the light energy flow. ! Light rays travel in straight lines forever unless it interacts with matter (reflection, refraction, scattering, and absorption). ! Light rays can cross without interacting with each other. ! Each point of an object is a source of light rays. ! The eye sees by focusing a bundle of rays. 18.1 Sources of light rays

! Self-luminous objects (or sources) directly create light rays. ! A ray source emits a single ray. ! A point source emits light rays in all direction. ! An extended source emits light from an extended surface. ! A parallel-ray source produces a bundle of parallel rays.

! Reflective objects reflect rays originating from self-luminous objects. 18.1 Ray diagrams

! A ray diagram is a diagram that shows a few light rays in order to simplify the situation. 18.1 Seeing objects / Demo

! In order for our eye to see an object, rays from that object must enter the eye.

! Demo: Laser and chalk dust 18.1 Shadows

! An opaque object can intercept rays, creating a shadow behind it.

! A point source creates a completely dark shadow with a sharp edge.

! An extended source often creates a true shadow that no light reaches, surrounded by a fuzzy region of increasing brightness. 18.2 Reflection

! Specular reflection is the reflection from a smooth surface.

! The incident and reflected rays and the normal lie on the same plane, and the law of reflection states:

!" = !$ 18.2 Diffuse reflection

! Reflection from a rough surface is diffuse reflection.

! 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. 18.2 The plane mirrors

! A plane mirror is a flat mirror.

! The virtual image of P is at Point P!. " ! The image distance ! is equal to the object distance !:

!" = ! Quiz: 18.2-1

! An observer at point O is facing a mirror and observes a light mirror source S. Where does the O observer perceive the mirror image of the source to be located? S Quiz: 18.2-1 answer / Demo

! Trace the light rays from the object to the mirror to the eye. mirror

! Since the brain assumes that light O travels in a straight line, simply extend the rays back behind the mirror to locate the image.

! Demo: Location of image S Quiz: 18.2-2

! At a hair salon, you are trying to see back of your head. You hold a hand 1.0 m 0.5 m mirror 0.5 m in front of you and look at your reflection in a full-length mirror 1.0 m behind you. How far back of the hand mirror do you see the closest image of back of your head, in meters? Quiz: 18.2-2 answer

! 2.5 m

! The image of the head reflected in the big mirror appears 1.0 m behind the big mirror.

! This image (which is the object for the small mirror) is 2.5 m away from the hand mirror.

! The final image is 2.5 m behind the hand mirror.

1.0 m 1.0 m 0.5 m

Big mirror small mirror

Image of head Head Image of head in in big mirror small mirror

2.5 m 2.5 m 18.3 Refraction

! Refraction is a change in direction of light as it transmits from one medium to another. ! Light travels from one point to another along the path that takes least time.

! Angle of refraction is the angle of transmitted ray, !". ! The angles of incidence and refraction, and indices of refraction of two media are related by Snell’s Law:

#$ sin !$ = #" sin !"

Lifeguard analog Quiz: 18.3-1

! 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 A. directly at the point where you see the fish. B. slightly above the point where you see the fish. C. slightly below the point where you see the fish. Quiz: 18.3-1 answer

! 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. ! Follow-up: To shoot a fish with a laser gun instead, should you aim directly at the image, slightly above, or slightly below? Total internal reflection / Demo

! If !" < !$, total internal reflection (TIR) occurs when the incident angle is greater than the critical angle, %&, and no refracted ray exists.

!" sin %& = !$

! Demo: TIR Quiz: 18.3-2

! A laser beam undergoes two refractions at the interface between medium 1 and 2, and total internal reflection at the interface between medium 2 and medium 3 as shown. Rank the indices of refraction of media 1, 2, and 3, smallest first. Quiz: 18.3-2

! !" < !$ < !% ! Since there is TIR at the the interface between medium 2 and medium 3, !" < !$. ! Since the angle of the ray in medium 1 is smaller than the angle in medium 2, !$ < !% from Snell’s law: !% sin )% = !$ sin )$. Quiz: 18.3-3

! In an optical fiber, what can be said about the index of refraction of the core, !"#$%, versus the index of refraction of the cladding, !"&'(()*+? Quiz: 18.3-3 answer / Demo

! !"#$%%&'( < !"*+,

! In order for there to be total internal reflection light must travel in a higher index of refraction and incident on a boundary with medium of a lower index of refraction.

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

! Endoscopes made from optical fibers are used for anthroscopic surgery.

! Demo: Fiber optics