Topics

1. Topics • 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.

2. The principle of finding a focal point Incoming parallel light rays Exiting light rays Reflecting or refracting object Focal point

3. The principle of finding a focal point Incoming parallel light rays Exiting light rays Reflecting or refracting object Focal point

4. Determination of the radius of a spherical mirror Concave mirror, reflecting side here. R x D

5. …alternative method… Polar graph paper 90 135 45 Move mirror until curvature matches the curvature on polar graph paper. then measure R as shown. 180 0 R 135 45 90

6. Convex versus concave Concave Mirror: Convex Mirror:

7. Convex versus concave Concave Lens: Convex Lens:

8. Convex versus concave Plano Concave Lens: Plano Convex Lens:

9. Convex versus concave Convex Concave Lens:

10. The Spherical Mirror Equation So: object distance Si: image distance R: radius of curvature of spherical mirror f: focal length of spherical mirror

11. Sign Convention for Spherical Mirrors P F S C V f si R so Sign Convention for Mirrors

12. Refraction on a single spherical surface n1 n2

13. Single Spherical Surface  n1: index of refraction on one side of the surface n2: index of refraction on the other side of the surface R: radius of curvature of the surface f1 : focal distance in first medium f2 : focal distance in second medium so : object distance si : image distance

14. Determining the two focal distances for a spherical surface Fo V Note that Hecht names f1 and f2 differently: Instead of f1 he used fo as in “object focal distance” Instead of f2 he uses fi as in “image focal distance” fo V Fi C fi

15. Sign Conventions (according to Hecht) Sign Convention for Spherical Refracting Surfaces and Thin Lenses (Light Entering from the Left) Fo V fo C Fi V fi fi

16. Practical way of making a single spherical surface Focus still in the plastic Rectangular plastic Semi-circular plastic

17. 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) R1 is the curvature on the left side. R2 is the curvature on the right side.

18. Examples C2 C1 V1 V2 R2 positive (C2 to the right of V2) R1 negative (C1 to the left of V1)

19. Examples C1 C2 V2 V1 R2 negative (C2 to the left of V2) R1 positive (C1 to the right of V1)

20. Thick Lenses: Measuring focal distances and principal planes

21. Thick Lenses: Measuring focal distances and principal planes

22. 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.