1. Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES  Measuring: Radii of mirrors and lenses Focal points of mirrors, spherical surfaces, thin lenses Focal points and principal planes for thick lenses  Comparison to theory: Spherical mirror equation Relation for single spherical surface Lens maker’s formula (thin lenses) Equations for focal length and principal planes (thick lenses)  Practicing: Sign conventions for radii and focal points of curved reflecting and refracting surfaces. Topics

2. Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES The principle of finding a focal point Reflecting or refracting object Incoming parallel light raysExiting light rays Focal point

3. Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES The principle of finding a focal point Reflecting or refracting object Incoming parallel light raysExiting light rays Focal point

4. Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES R D x Concave mirror, reflecting side here. Determination of the radius of a spherical mirror

5. Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES 180  Polar graph paper …alternative method… R 00 45  90  135  Move mirror until curvature matches the curvature on polar graph paper. then measure R as shown.

6. Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES Convex versus concave Concave Mirror : Convex Mirror :

7. Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES Convex versus concave Concave Lens : Convex Lens :

8. Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES Convex versus concave Plano Concave Lens : Plano Convex Lens :

9. Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES Convex versus concave Convex Concave Lens :

10. Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES The Spherical Mirror Equation S o : object distance S i : image distance R: radius of curvature of spherical mirror f: focal length of spherical mirror

11. Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES Sign Convention for Mirrors Sign +- soso Left of V, real objectRight of V, virtual object sisi Left of V, real imageRight of V, virtual image f Concave mirrorConvex mirror R C right of V, convexC left of V, concave yoyo Above axis, erect objectBelow axis, inverted object yiyi Above axis, erect imageBelow axis, inverted image Sign Convention for Spherical Mirrors C S P F V f sisi R soso

12. Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES Refraction on a single spherical surface n1n1 n2n2

13. Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES Single Spherical Surface n 1 : index of refraction on one side of the surface n 2 : index of refraction on the other side of the surface R: radius of curvature of the surface f 1 : focal distance in first medium f 2 : focal distance in second medium s o : object distances i : image distance 

14. Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES Determining the two focal distances for a spherical surface FiFi C V V FoFo fofo fifi Note that Hecht names f 1 and f 2 differently: Instead of f 1 he used f o as in “object focal distance” Instead of f 2 he uses f i as in “image focal distance”

15. Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES Sign Conventions (according to Hecht) FiFi C V V FoFo fofo fifi fifi Sign Convention for Spherical Refracting Surfaces and Thin Lenses (Light Entering from the Left) s o, f o +left of V xoxo +left of F o s i, f i +right of V xixi +right of F i R +if C is right of V y o, y i + above the optical axis

16. Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES Practical way of making a single spherical surface Semi-circular plastic Rectangular plastic Focus still in the plastic

17. Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES Lens Maker’s Equation (for thin lenses) Use proper conventions: R is positive if center of curvature (C) is to the right of vertex (V) R is negative if center of curvature (C) is to the left of vertex (V) R 1 is the curvature on the left side. R 2 is the curvature on the right side.

18. Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES Examples R 1 negative (C 1 to the left of V 1 ) C1C1 C2C2 V1V1 V2V2 R 2 positive (C 2 to the right of V 2 )

19. Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES Examples R 1 positive (C 1 to the right of V 1 ) C2C2 C1C1 V1V1 V2V2 R 2 negative (C 2 to the left of V 2 )

20. Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES Thick Lenses: Measuring focal distances and principal planes

21. Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES Thick Lenses: Measuring focal distances and principal planes

22. Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES Thick Lens Equations: You can now use simple lens equations as long as all distances are measured from the principal planes instead of the center of the lens.