Lenses & Optical Instruments

1. Lenses & Optical Instruments

2. Outline • Thin Lenses; Ray Tracing • The Thin Lens Equation; Magnification • Combinations of Lenses • Lensmaker’s Equation • Cameras: Film and Digital • The Human Eye; Corrective Lenses • Magnifying Glass • Telescopes • Compound Microscope • Aberrations of Lenses and Mirrors

3. Thin Lenses; Ray Tracing Thin lenses are those whose thickness is small compared to their radius of curvature. They may be either converging (Fig. a) or diverging (Fig. b). Fig. b Fig. a

4. Thin Lenses; Ray Tracing Thin lens:A lens with a small thickness compared to the radius of curvature. May be either Converging (Fig. a) or Diverging(Fig. b)

5. Converging Lens A lens that is thicker in the center than at the edge. Parallel rays are brought to a focus by a converging lens.

6. Diverging LensA lens that is thicker at the edge than in the center. A diverging lens makes parallel light diverge. The focal point is that point where the diverging rays would converge if they were projected back.

7. The Power of a lens is defined to be the inverse of its focal length: Lens Power is measured in diopters, D: 1 D  1 m-1.

8. Image Formation by Converging Lenses • Just as for mirrors, for lenses,Ray diagramsare used to determine where an image will be. For lenses,3 key rays, each beginning on the object, are used: • Ray 1:Comes in parallel to the axis & exits through the focal point. • Ray 2:Comes in through the focal point & exits parallel to the axis. • Ray 3:Goes through the center of the lens & is undeflected. • See the figures on the next slide!

9. Three key rays, each beginning on the object, are used: Ray 1: Leaves a point on the object going parallel to the axis & refracts through focal point F behind the lens. Ray 2: Leaves a point on the object, passes through F' in front of the lens & refracts parallel to the axis behind it. Ray 3: Leaves a point on the object & passes through the lens center.

10. Conceptual Example A half-blocked lens. What happens to the image of an object if the top half of a lens is covered by a piece of cardboard (Fig. a)? Fig. a Fig. b Answer:An image will still be visible, but it will be less bright than it would be without the blockage. (Fig. b)

11. To analyze a diverging lens, use The same 3 Rays. The image will be upright and virtual.

12. The Thin Lens Equation; Magnification The thin lens equation is similar to the mirror equation:

13. The Sign Conventions are slightly different for lenses than for mirrors. • The focal length is positive for converging lenses & negative for diverging lenses. • The object distance is positive when the object is on the same side as the light entering the lens (not an issue except in compound systems); otherwise it is negative. • The image distanceis positive if the image is on the opposite side from the light entering the lens; otherwise it is negative. • The height of the image is positive if the image is upright & negative otherwise.

14. The Magnification Formula is also the same as that for a mirror: The power of a lens is positive if it is converging and negative if it is diverging.

15. Problem Solving Thin Lenses • Draw a ray diagram.The image is located where the key rays intersect. • Solvefor the unknowns. • Follow the sign conventions. • Check that your answers are consistent with the ray diagram.

16. Example Image formed by converging lens. Calculate(a)The Position, & (b)The Size, of the image of a 7.6-cm-high leaf placed 1.00 m from a +50.0-mm focal-length camera lens.

17. Example: Object close to a converging lens.An object is placed 10 cm from a 15-cmfocal-length converging lens.Calculate the Image Position & Size(a) Analytically, & (b) Using a ray diagram.

18. Example: Diverging lens. Where must a small insect be placed if a 25-cm focal-length diverging lens is to form a virtual image 20 cm from the lens, on the same side as the object? See the figure.