General Physics II Mirrors & Lenses Nothing New! For the next several lectures we will be studying geometrical optics. You already know the fundamentals of what is going on!!! Light propagates as rays in situations in which the length scales are >> than the light’s wavelength Reflection: incident ray θ1 = θr Refraction: θ1 θr θ2 n1 sinθ1 = n2 sinθ2 reflected ray n1 n2 refracted ray • We will use these laws to understand the properties of mirrors (perfect reflection) and lenses (perfect refraction). • We will also discover properties of combinations of lenses which will allow us to understand such applications as microscopes, telescopes, and eyeglasses. Page 1 Images formed by mirrors and lenses may be classified as real or virtual virtual.. Real Image formed by actual rays of converging light Virtual Image not formed by actual rays of converging light, but from where the rays of light appear to come (diverging light rays) Reflection at a plane surface The reflected rays entering eyes look as though they had come from image P’. P’ virtual image P Light rays radiate from a point object at P in all directions. Page 2 do di ho hi image is erect image is virtual M = hi/ho=1 lateral magnification di = do Curved Mirrors Terminology center of curvature - C; the center of the original sphere radius of curvature - r; distance from center of curvature to the mirror vertex - V; the center of the mirror principal axis - a line through C and V principal focus - F; the point on the principal axis where light rays parallel and close to the principal axis converge; or from where they appear to diverge focal length - f; distance from V to F V V Convex Concave Page 3 Concave Spherical Mirrors We start by considering the reflections from a concave mirror in the “paraxial” approximation (i.e., small angles of incidence close to a single axis): • Parallel Ray: Draw a ray from the tip of the arrow parallel to the axis. It passes through the ‘focal point’ (F) of the mirror. • Focal Ray: Draw a ray from the tip of the arrow through the focal point. This ray is reflected back parallel to the axis. C F • Principle Ray: Draw a ray from the tip of the arrow through the center of curvature (C). This ray is reflected straight back since the angle of incidence = 0o. The diagram below shows three light rays reflected off of a concave mirror. Which ray is NOT correct? R A) C) B) Page 4 f Similarly for a Convex Spherical Mirror The Mirror Equation 1 1 1 + = s s′ f h f h’ s’ s h s h’ Now, we can introduce a sign convention. We can indicate that this image is inverted if we define its magnification M as the negative number given f by: s’ M =− Page 5 s′ s Lenses A lens is a piece of transparent material shaped such that parallel light rays are refracted towards a point, a focus: Convergent Lens (Convex) » light moving from air into glass will move toward the normal » light moving from glass back into air will move away from the normal » real focus Positive f Negative f Divergent Lens (Concave) » light moving from air into glass will move toward the normal » light moving from glass back into air will move away from the normal » virtual focus The Convex Converging Lens Ray Trace: • Parallel Ray: Draw a ray from the tip of the arrow parallel to the axis. Upon REFRACTION, it passes through the ‘focal point’ on the opposite side of the lens. • Focal Ray: Draw a ray from the tip of the arrow through the focal point on the same side of the lens. Upon REFRACTION, this ray moves parallel to the axis. • Chief Ray: Draw a ray from the tip of the arrow through the center of the lens. Upon REFRACTION, this ray continues straight along its original path. Page 6 Similarly for a Concave Divergent vergent Lens The Lens Equation….same as the Mirror h s’ s f h’ 1 1 1 + = s s′ f M =− Page 7 s′ s End of Mirrors & Lenses Lecture Page 8