Lenses

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

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

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

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.

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.

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.

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

Image Formation by Converging Thin Lens 1 Real Image 3 Principle Axis 2F F F 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.

Image Formation by Converging Thin Lens Real Image 1 3 Principle Axis 2F F F 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.

Image Formation by Converging Thin Lens 1 Principle Axis 2F F F 2F 2 Virtual Image Object 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.

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).

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

The Thin Lens Equations 1 1 1 do di f 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 + = m = = -

Example 1 Image hi Principle Axis 2F F F 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

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

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.

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.

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.