Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Mirrors and Lenses

Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Curved Mirror u Parallel light rays reflect off of a curved mirror and converge at a Focal Point u C is the Center of Curvature for the curved mirror u F is the Focal Point for incoming parallel light Axis of symmetry Light Rays F’ C

Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Review: Snell’s Law u The change in direction is described by Snell’s Law. u This change is dependent upon the index of the material (optical density) and is relative to the normal line. AIR GLASS AIR GLASS normal

Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Snell’s Law Snell’s Law: n 1 sin  1 = n 2 sin  2 11 22 n1n1 n2n2 (Or, if  1 and  2 are small, n 1  1 = n 2  2 )

Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Refraction for Different Materials  AIR WATER GLASS DIAMOND    light

Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Flat to Curved () Surface Flat to Curved (transmissive) Surface A curved surface can be approximated with small straight segments.

Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Graphical Ray Tracing u A way to analyze optical systems. u Modern ray tracing is often done on a computer u Light rays always travel from left to right for analysis purposes. Axis of symmetry Image side (+)Source side(-) Light Rays Lens

Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Curved Interface u Concave interface diverges rays. u Convex interface converges rays. Assuming n’ > n nn’n

Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Convex Lens shorthand In real life Double Convex Plano-Convex Positive Meniscus Types

Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Convex Lens u Image focal point, F’, is half the distance to the effective center of curvature of the lens. u Object focal point, F, is exactly the same distance on the object side of the lens. Axis of symmetry Light Rays Lens F’ F Object side Image side

Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Convex Lens u Image focal length, f’, is the distance from the lens to the image focal point. u Object focal length, f, is the distance from the lens to the object focal point. F’ f’ F f

Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Ray Diagrams for a Positive (Convex) Lens  (infinity) Object Location Image Type and Location Real, at F’ F Real, at 2F’ Real, at  (infinity) Virtual 2F < F

Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Real vs. Virtual Images u Real Image: Image formed where light rays actually converge and pass through a specific point. Real images can be projected onto paper or a screen. u Virtual Image: Image formed where light rays appear to diverge from. Virtual images cannot be projected onto paper or a screen.

Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Concave Lens shorthand In real life Double concave Plano- concave Negative meniscus Types

Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Concave Lens u Image focal point, F’, is on the object side u Focal length, f’, is negative. Axis of symmetry Light Rays Lens F’ f’

Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Ray Diagrams for a Negative (Concave) Lens Rays converging toward F Object Location Image Type and Location Virtual, at  (infinity) Approaching the lens from  (infinity) Virtual, at F’ Virtual, between F’ and the lens  (infinity)

Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Aberrations u Spherical lenses and mirrors, even if ground and polished perfectly, do not produce perfect images. u The deviation in the image is called an aberration.

Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Chromatic Aberration u Dispersion results in a lens having different focal points for different wavelengths - this effect is called chromatic aberration. u Results in a “halo” of colors. u Solution: Use 2 lenses of different shape and material (“achromatic doublet”). F’ Red. Object (small dot)Image with chromatic aberration F’ Blue White light

Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Spherical Aberration u All the rays do not bend toward the focal point, resulting in a blurred spot. u Solution: use lenses with aspherical curvature, or use a compound lens. F’. Object (small dot)Image with spherical aberration

Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Other Aberrations u Coma u Off axis blur which looks like the “coma” of a comet. u Astigmatism u Different focal lengths for different planes. u Distortion u Images formed out of shape...