Lenses

1. Lenses

2. Refraction of Light • When light travels through a surface between two different media, the light will be refracted if the angle of incidence is greater than zero. • If light is passing into a more dense media, it will bend towards the normal. www.hyperphysics.phy-astr.gsu.edu

3. Law of Refraction (Snell’s Law) • The ratio of the sine of the angle of incidence to the angle of refraction is a constant. n1 sin1 = n2 sin2 Where: n1, n2 = index of refraction 1= Angle of incidence 2 = Angle of refraction speed of light in a vacuum c speed of light in the material v n = = www.sol.sci.uop.edu

4. Light Passing Through Glass Air Air Glass Reflected Ray Refracted Ray θ4 θ2 θ3 θ1 Incident Ray Note: 1 = 4 2 = 3

5. Lenses and Their Uses • Eyeglasses first made around the 13th century. • Galileo used them as a telescope to discover the moons of Jupiter and the phases of Venus. • Other applications include microscopes, overhead projectors and cameras. • A special type of lens, called the fresnel lens, is used in lighthouses, traffic lights, rear windows of motor homes and overhead projectors.

6. Definition of a Lens • What is a lens? • A lens is made of a transparent material such as glass or plastic such that the index of refraction is greater than that of air.

7. Types of Thin Lenses • What types of lenses are there? • Convex (Converging): A lens that is thicker in the middle than at the edges. Converging lenses cause incident parallel rays to converge at a point. • Concave (Diverging): A lens that is thinner in the middle than at the edges. Diverging lenses cause parallel rays of light to diverge when leaving the lens. • Fresnel: A lens comprised of rings of glass prisms positioned above and below a lamp to bend and concentrate light into a bright beam.

8. Converging and Diverging Thin Lenses • Convex/Converging Lens: • Concave/Diverging Lens: 1 Focal point 3 Principle Axis F F 2F 2F 2 Focal point 1 2 3 F F

9. Image Formation by Converging Thin Lens 1 Real Image 3 Principle Axis F F 2F 2F 2 Object • An object placed more than 2X the focal distance before the lens will produce an inverted and smaller real image. • This type of lens is similar to those used in cameras.

10. Image Formation by Converging Thin Lens Real Image 1 3 Principle Axis F F 2F 2F 2 Object • An object placed between F and 2F will produce an inverted and larger real image. • This type of lens is similar to those used in projectors.

11. Image Formation by Converging Thin Lens 1 Principle Axis F F 2F 2F 2 Object Virtual Image • An object placed between F and the lens will produce an upright and larger virtual image. • This type of lens is similar to a magnifying lens.

12. Image Formation by Diverging Thin Lens 1 2 3 F F Virtual Image Object • A diverging lens always produces a virtual image that is upright and smaller than the object. • This type of lens is used in glasses to correct for myopia (near sighted).

13. Image Formation for Converging and Diverging Thin Lenses • Image formation for diverging lenses. • Image formation for converging lenses.

14. + = m = = - The Thin Lens Equations 1 1 1 do dif Where: do and di are the distances of the object and image from the mirror, respectively. f = focal length. Image height, hi di Object height, ho do

15. Example 1 Image hi Principle Axis F F 2F 2F hi Object f do di • An object is placed at a distance of 6 cm from a converging lens. The focal length of the lens is 2 cm. The distance of the image to the lens is: a. 1.0 cm b. 1.5 cm c. 3.0 cm d. 4.5 cm e. 6.0 cm

16. Example 2 & 3 • An object is placed between the focal point and twice the focal length of a converging lens. The image formed will be: a. real and upright b. real and inverted c. virtual and upright d. virtual and inverted e. located at the focal length • An object is placed at a distance of 20 cm from a converging lens. The resulting image appears at a distance of 80 cm from the lens. The image is magnified by a factor of: a. 0.25 b. 4.0 c. 8.0 d. 12.0 e. 16.0

17. Sign Conventions for Thin Lenses • Focal Length • f is positive for a converging lens. • f is negative for a diverging lens. • Object Distance • do is + if the object is to the left of the lens (real object). • do is - if the object is to the right of the lens (virtual object). • Image Distance • di is + for an image (real) formed to the right of the lens by a real object to the left. • di is – for an image (virtual) formed to the left of the lens by a real object. • Magnification • m is + for an image that is upright with respect to the object. • m is – for an image that is inverted with respect to the object.

18. Key Ideas • Snell’s Law / Law of Refraction: Light will bend toward the normal when transitioning from a media with a low index of refraction (e.g. air) to a media with a higher index of refraction. • Paraxial light rays parallel to the principle axis of a converging lens will come to a point called the focus. • Paraxial light rays parallel to the principle axis of a diverging lens will appear to have originated from a point called the focus. • Diverging lenses always form virtual images.

19. Key Ideas • The thin lens equation can be used to determine the distance an image forms from a lens and is the same as that used for spherical mirrors. • Ray diagrams can be used to determine where images will form.