# Geometric!Op9cs! Reflec9on! Refrac9on!`!Snell s!law! Mirrors!and!Lenses! Other!topics! Thin!Lens!Equa9on! Magnifica9on! Lensmaker s!formula!

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1 Geometric!Op9cs! Reflec9on! Refrac9on!`!Snell s!law! Mirrors!and!Lenses! Thin!Lens!Equa9on! Magnifica9on! Lensmaker s!formula! Other!topics! Telescopes! Apertures!

2 Reflec9on! Angle!of!incidence!equals!angle!of!reflec9on! θ in!=!θ out!

3 Snell s!law! Relates!angle!of!incidence!to!angle!of!refrac9on! n!represents!refrac&on)index!of!material' Can!change!depending!on!light!wavelength!

4 Snell s!law! 97. A beam of light has a small wavelength spread d l about a central wavelength l. The beam travels in vacuum until it enters a glass plate at an angle q relative to the normal to the plate, as shown in the figure above. The index of refraction of the glass is given by n( l ). The angular spread dq of the refracted beam is given by (A) dq 1 n dl (B) dq dn ( l) dl dl 1 dl (C) dq dl l dn (D) dq sin q sin q dl l (E) dq tan q dn( l) n dl dl

5 Thin!Lens!Equa9on! This!is!the!only!equa9on!you!need,!provided!you! can!interpret!it!correctly! O!=!object!distance!from!lens! I!=!image!distance!from!lens! F!=!focal!point!distance!from!lens!

6 Thin!Lens!!Geeng!Signs!Right! Sign conventions (why this is nontrivial) A is where light comes from, B is where light passes to Note side B is different for mirrors and lenses

7 Thin!Lens!!Geeng!Signs!Right! Recommend!picking!on!case!to!memorize! O!>!0! F!>!0! I!=!?!

8 Thin!Lens!Example! 74. The figure above shows an object O placed at a distance R to the left of a convex spherical mirror that has a radius of curvature R. Point C is the center of curvature of the mirror. The image formed by the mirror is at (A) infinity (B) a distance R to the left of the mirror and inverted (C) a distance R to the right of the mirror and upright (D) a distance R 3 to the left of the mirror and inverted (E) a distance R 3 to the right of the mirror and upright

9 Thin!Lens!Example!!Ray!Diagram! Draw!rays!to!get!qualita9ve!sense!of!image! Rays!from!object!to!focus!reflect!parallel! Parallel!rays!from!object!reflect!from!focus! Rays!from!object!to!center!reflect!at!equal!angle! Same!deal!for!lenses,!but!with!passing!through!!

10 Example!Ray!Diagrams!`!Lenses! h]p://hyperphysics.phy`astr.gsu.edu/%e2%80%8chbase/geoopt/raydiag.html!

11 Magnifica9on! Magnifica9on!is!image!size!rela9ve!to!object! Image!is! imaginary!if!not!in!real!space!(i!<!0)! Image!is! real!if!projected!into!real!space!

12 One!more!example:!Mul9ple!Lenses! Treat the image from the first lens as a virtual object 1. Find the image from the first lens 2. Use geometry to find O for the second lens 3. Apply lens equation a second time 11. An object is located 40 centimeters from the first of two thin converging lenses of focal lengths 20 centimeters and 10 centimeters, respectively, as shown in the figure above. The lenses are separated by 30 centimeters. The final image formed by the two-lens system is located (A) 5.0 cm to the right of the second lens (B) 13.3 cm to the right of the second lens (C) infinitely far to the right of the second lens (D) 13.3 cm to the left of the second lens (E) 100 cm to the left of the second lens

13 Mul9ple!lenses! 11. An object is located 40 centimeters from the first of two thin converging lenses of focal lengths 20 centimeters and 10 centimeters, respectively, as shown in the figure above. The lenses are separated by 30 centimeters. The final image formed by the two-lens system is located (A) 5.0 cm to the right of the second lens (B) 13.3 cm to the right of the second lens (C) infinitely far to the right of the second lens (D) 13.3 cm to the left of the second lens (E) 100 cm to the left of the second lens First lens: O = 40 cm, F = 20 cm, I =? Second lens: F = 10 cm, O =?, I =?

14 Lensmaker s!formula! Find!the!focal!point,! given!the!radii!of!the! two!faces!of!the!lens! 15. If the five lenses shown below are made of the same material, which lens has the shortest positive focal length? (A) (B) (C) (D) (E) h]p://hyperphysics.phy`astr.gsu.edu/hbase/hframe.html!

15 Telescopes! Telescope angular magnification f E : Focal length of eyepiece f O : Focal length of objective Note: The two lenses share a focal point

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