1. Module 1-4 Basic Geometrical Optics

2. Image Formation with Lenses Lenses are at the heart of many optical devices, not the least of which are cameras, microscopes, binoculars, and telescopes. Lenses are essentially light-controlling elements, used primarily for image formation with visible light, but also for ultraviolet and infrared light.

3. Image Formation with Lenses Function of a lens A lens is made up of a transparent refracting medium, generally of some type of glass, with spherically shaped surfaces on the front and back. A ray incident on the lens bends at the front surface, propagates through the lens, and bends again at the rear surface, according to Snell’s law. See Figure 1, next slide

4. Image Formation with Lenses Figure 1: Refraction of light rays by a lens where: n = index of refraction t = axial thickness

5. Image Formation with Lenses Types of lenses If the axial thickness t of a lens (see Figure 1) is small compared with the radii of curvature r 1 and r 2 of its surfaces, it can be treated as a thin lens. If the thickness of a lens is not negligible compared with the radii of curvature of its faces, it must be treated as a thick lens. NOTE: In this basic introduction of geometrical optics, however, we shall deal only with thin lenses.

6. Image Formation with Lenses Converging and diverging thin lenses In Figure 2, are shown shapes of several common “thin” lenses. Figure 2

7. Image Formation with Lenses Focal points of thin lenses The focal points of lenses are defined in terms of the effect that lenses have on incident parallel light rays and plane wave fronts. Figure 3 shows parallel light rays and their associated plane wave fronts incident on a positive lens (Figure 3a) and a negative lens (Figure 3b).

8. Image Formation with Lenses Figure 3a Positive lens

9. Image Formation with Lenses Figure 3b Negative lens

10. Image Formation with Lenses For the positive lens, refraction of the light by the lens brings it to a focal point F (real image) to the right of the lens. For the negative lens, refraction of the light by the lens causes it to diverge as if it were coming from focal point F located to the left of the lens.

11. Image Formation with Lenses For thin lenses, there are two focal points, symmetrically located on each side of the lens, since light can approach from either side of the lens. Figure 4a two focal points, for positive lenses

12. Image Formation with Lenses Figure 4b two focal points, for negative lenses

13. Image Formation with Lenses Lens formulas for thin lenses For thin lenses convenient formulas can be used to locate the image mathematically. Figure 5 shows the essential elements that show up in the final equations, relating object distance p to image distance q, for a lens of focal length f with radii of curvature r 1 and r 2 and refractive index n g. For generality, the lens is shown situated in medium of air with refractive index n = 1

14. Image Formation with Lenses Figure 5 Defining quantities for image formation with a thin lens

15. Image Formation with Lenses Equations for thin lens calculations where p (d o ) is the object distance (from object to lens vertex V ) q (d i ) is the image distance (from image to lens vertex V ) f is the focal length (from either focal point F or F ' to the lens vertex V )

16. Image Formation with Lenses Equations for magnification calculations where m is the magnification produced by the lens (ratio of image size to object size) h i is the vertical transverse size of the image, measured perpendicularly to the optical axis h o is the vertical transverse size of the object, measured perpendicularly to the optical axis p and q are object and image distance respectively