Lenses & Optical Instruments Chapter 33 opener. Of the many optical devices we discuss in this Chapter, the magnifying glass is the simplest. Here it is magnifying part of page 886 of this Chapter, which describes how the magnifying glass works according to the ray model. In this Chapter we examine thin lenses in detail, seeing how to determine image position as a function of object position and the focal length of the lens, based on the ray model of light. We then examine optical devices including film and digital cameras, the human eye, eyeglasses, telescopes, and microscopes.

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

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). Figure 33-2. (a) Converging lenses and (b) diverging lenses, shown in cross section. Converging lenses are thicker in the center whereas diverging lenses are thinner in the center. (c) Photo of a converging lens (on the left) and a diverging lens (right). (d) Converging lenses (above), and diverging lenses (below), lying flat, and raised off the paper to form images. Fig. b Fig. a

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) Figure 33-2. (a) Converging lenses and (b) diverging lenses, shown in cross section. Converging lenses are thicker in the center whereas diverging lenses are thinner in the center. (c) Photo of a converging lens (on the left) and a diverging lens (right). (d) Converging lenses (above), and diverging lenses (below), lying flat, and raised off the paper to form images.

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. Figure 33-3. Parallel rays are brought to a focus by a converging thin lens.

Diverging Lens  A lens that is thicker at the edge than in the center 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. Figure 33-5. Diverging lens.

Lens Power is measured in diopters, D: 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.

Image Formation by Converging Lenses Just as for mirrors, for lenses, Ray diagrams are 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!

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. Figure 33-6. Finding the image by ray tracing for a converging lens. Rays are shown leaving one point on the object (an arrow). Shown are the three most useful rays, leaving the tip of the object, for determining where the image of that point is formed. Ray 3: Leaves a point on the object & passes through the lens center.

Answer: An image will still be visible, but it will be less bright 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)? Solution: The image is unchanged (follow the rays); only its brightness is diminished, as some of the light is blocked. 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)

To analyze a diverging lens, use The same 3 Rays To analyze a diverging lens, use The same 3 Rays. The image will be upright and virtual. Figure 33-8. Finding the image by ray tracing for a diverging lens.

The Thin Lens Equation; Magnification The thin lens equation is similar to the mirror equation: Figure 33-9. Deriving the lens equation for a converging lens.

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 distance is 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.

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.

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

Image formed by converging lens. 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. Solution: The figure shows the appropriate ray diagram. The thin lens equation gives di = 5.26 cm; the magnification equation gives the size of the image to be -0.40 cm. The signs tell us that the image is behind the lens and inverted.

Example: Object close to a converging lens Example: Object close to a converging lens. An object is placed 10 cm from a 15-cm focal-length converging lens. Calculate the Image Position & Size (a) Analytically, & (b) Using a ray diagram. Figure 33-12. An object placed within the focal point of a converging lens produces a virtual image. Example 33–3. Solution: a. The thin lens equation gives di = -30 cm and m = 3.0. The image is virtual, enlarged, and upright. b. See the figure.

Example: Diverging lens 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. Solution: Since the lens is diverging, the focal length is negative. The lens equation gives do = 100 cm.