What Happens When… Light is transmitted through a glass shaped like a triangle? Light is transmitted straight toward a glass shaped like a square?

What happens when we put them together? If we soften the edges, we get a lens that converges light to a single point.

Thin Lenses Objectives: • Identify the basic properties of thin lenses, such as the focal point, focal length, and the center of curvature. • Calculate the location of the image of a specified object as formed by a double convex and double concave lens and determine the magnification and character of the image for each case. • Construct ray diagrams to determine the location and nature of the image of a given object when geometric characteristics of the optical device are known.

Lenses! A carefully ground or molded piece of transparent material that refracts light rays to form an image. It is the believed that the earliest might be from 640 B.C. Rock lens found in Nineveh. More commonly used beginning in the 11th century. Reading stones Glasses replaced reading stones in the 13th century.

Types of Lenses Lenses differ in terms of their shape and the materials from which they are made. They typically have a circular shape with two spherical surfaces. Each surface can be convergent, divergent, or planar. We are going to only look at double lenses. Convergent is a biconvex lens. Divergent is a biconcave lens.

Similar To The Mirrors! Convergent Light from a distant source is concentrated at the focal point. Remember! Light from a distant source is assumed to be parallel!

Similar To The Mirrors! Divergent Light from a distant source looks like it comes from the focal point.

Double The Fun! Each lens within a double lens has its own radius of curvature and its own focal length. The focal lengths of each lens DOES NOT have to be the same. To keep it simple, we will only look lenses where the focal lengths are equal.

Where’s The Image? Enlarged or reduced Inverted or upright To find an image for a lens, we construct ray diagrams like we do with mirrors. Since a lens is made out of glass, the rays of light pass through the lens and refract. When describing an image for a lens, we use the same three characteristics we used for mirrors. Enlarged or reduced Inverted or upright Virtual or Real When does a real image form? When the rays of light converge on the side of the lens opposite the source of light.

Constructing Ray Diagrams Where the three rays intersect is the location of the image. • M < 1 • Inverted • Real R R Ray 1: Drawn parallel to central axis and refracted through the focal point of Lens 1. Ray 2: Drawn through the focal point of Lens 2 and refracts parallel to the central axis. Ray 3: Drawn straight through the center of the lens.

Constructing Ray Diagrams Where the three rays intersect is the location of the image. • M > 1 • Upright • Virtual R R Ray 1: Drawn parallel to central axis and refracted through the focal point of Lens 1. Ray 2: Drawn in line with the focal point of Lens 2 and refracts parallel to the central axis. Ray 3: Drawn straight through the center of the lens.

Constructing Ray Diagrams Where the three rays intersect is the location of the image. • M < 1 • Upright • Virtual R R Ray 1: Drawn parallel to central axis and refracted away in line with the focal point of Lens 2. Ray 2: Drawn toward focal point of Lens 1 and refracts parallel to the central axis. Ray 3: Drawn straight through the center of the lens.

Analytical Methods Assuming that f1= f2 Sign Conventions: Lens Equation: 1 do di + f = Magnification (M): hi ho -di do = M = Convergent: f = positive Divergent: f = negative Sign Conventions: Height of the object (ho) is always positive. If image height is positive, it is upright. If image height is negative, it is inverted. Distance of object (do) is always positive. If the image distance is positive, it is real and on the opposite side of the lens from the object. If the image distance is negative, it is virtual and on the same side of the lens as the object.

Let’s Do An Example! You are taking a picture of a 7.6 cm flower that is 1.0 meter away. If your camera has a double convergent lens with a focal length of 50.0 mm, find the… 3 characteristics of the image Position of the image Size of the image Draw a Ray Diagram!!

The image is real, inverted, and has a M<1! Solve it! Info: ho = 7.6 cm do = 100 cm f = 5.0 cm 1 do di + f = - 1 do di f = - 1 di 5 cm = 100 cm di = 5.26 cm hi ho -di do = M = hi ho -di do = hi (7.6 cm) -(5.26 cm) 100 cm = hi = -.40 cm The image is real, inverted, and has a M<1!