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Chapter 23 - Geometric Optics

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McGill University
PHYS 101
Kenneth Ragan

Chapter 23 – Light: Geometric Optics 23.1 – The Ray Model of Light: Ray Model: light travels in a straight-line path called light rays  A ray represents an extremely narrow beam of light  Although light rays leave each point in many different directions, normally only a small bundle of these rays can enter the pupil of an observer’s eye  Geometric Optics: involve straight-line rays at various angles Exam Conceptual Question: Compare sound to light from a wave phenomena point of view 23.2 – Reflection; Image Formation by a Plane: When light strikes the surface of an object, some of the light is reflected. The rest can be absorbed by the object and then transformed into thermal energy. If the object is transparent like glass or water, part of the light can be transmitted through. Example: looking at a plane mirror  Light rays emitted from the object strike the mirror and are reflected in the observers eyes, therefore the observer sees that image as being “behind the mirror) When a narrow beam of light strikes a flat surface, we define the:  Angle of incident θ ti be the angle an incident ray makes with the normal to the surface  Angle of reflection, θ ro be the angle the reflected ray makes with the normal Law of Reflection: the angle of reflection equals the angle of incidence When you look in a mirror, you see an image of yourself and objects around you. You do not see yourself as others see you, because left and right appear reversed in the image. Image distance: distance from the mirror to the image Object distance: distance from the object to the mirror ** The height of the image is the same as that of the object Chapter 23 – Light: Geometric Optics Virtual image: the image would not appear on paper or film placed at the location of the image Real image: the light does pass through the image and therefore could appear on paper or film placed at the image position Clicker Question: The image of an object in a plane mirror is…always the same size as the object 23.3 – Formation of Images by Spherical Mirrors Convex: the reflection takes place on the outer surface of the spherical shape so that the center of the mirror surface bulges out toward the viewer  Example: the mirror on cars and trucks  Reduces the image size, includes a wide field of view Concave: the reflecting surface is on the inner surface of the sphere so that the center of the mirror sinks away from the viewer  Example: shaving or cosmetic mirrors  Magnified image Focal Point and Focal Length:  For a distant object, the rays from each point on the object that strike the mirror will be nearly parallel  For an object infinitely far away, the rays would precisely parallel  If the mirror is small compared to its radius of curvature, the reflected ray will only make a small angle with the incident ray, therefore the rays will cross each other at very nearly a single point, known as the focus  Focal Point: where incident parallel rays come to a focus after the center of the mirror  Focal Length: distance between the center of the mirror and the focal point Focal Length of Mirror: 𝒓 f =𝟐 Parabolic reflector: will reflect the rays to a perfect focus, parabolic shapes are much harder to make and thus much more expensive, spherical mirrors are used for this purpose Chapter 23 – Light: Geometric Optics 23.4 – Index of Refraction Refraction: change direction at the interface between two media (if the speed of light is different in the two media) The ratio of the speed of light in vacuum to the speed in a given material is called the index of refraction 𝒄 n = 𝒗 vlight c for all materials: n for all materials is larger than 1.0 So refraction occurs when light is incident on a boundary where the index of refraction changes. The index of refration n is often a slight function of the wavelength λ (colour) of the light. n(blue)
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