Lab 9: Geometrical optics Only 3 more labs to go!! Today we are going to do three experiments: 1. Measure the intensity of light as a function of distance away from its source. 2. Measure the focal length of a lens 3. Measure focal length of a mirror Light intensity (sometimes called illumination is defined as the amount of light energy falling on a certain area. The intensity of light from a source depends on two things: 1.The source (I.e. Laser vs. a candle) 2.The distance you are away from the source The equation for intensity is: where  is the amount of light energy emitted from the source and r is the distance you are away from the source I r NOTE: The intensity is directly proportional to the power of the source but inversely proportional to the SQUARE of the distance ln I ln r y-int = ln(  4  ) slope = 2

Mirrors: When light encounters a mirror it gets reflected. According the LAW OF REFLECTION the angle of reflection equals the angle of incidence FLAT MIRROR II RR  R =  I The LAW OF REFLECTION still holds true if the mirror has some shape to it. Look at this DIVERGING MIRROR (or sometimes called a CONVEX MIRROR)  R =  I Notice that if trace the reflected light rays back they seem to originate from a point behind the mirror. For this reason images viewed with diverging mirrors are always upright, smaller, and “virtual” Furthermore this focal length is related to the radius of curvature of the mirror by:

Converging mirrors (sometimes called concave) are opposite to diverging mirrors, they cause light rays to converge to a focus. The type of image this mirror produces depends on the position of the object relative to the focal point LENSES: LENS II RR tt When light encounters something transparent some of the light will be reflected as before. However, most of it will enter the transparent object and be refracted, or “bent”. Lenses allow light to enter the glass and be bent. If the transparent media is curved then we will have a lenses.

If the lens is thinner in the middle than at the edge, then it is a diverging lens The lens will diverge parallel light rays. The image viewed with a diverging lens will always be virtual, smaller, and upright. Diverging Lens Converging Lens If the lens is made such that it is thicker in the middle this will be a converging lens. This lens will focus incoming light rays to a point.

Ray tracing with lenses: Object X X f f 1 st : Draw a line through the middle lens 2 nd :Draw a line parallel to axis and make it pass through the focal point X X f f Notice how these rays never intersect. In this case you must the original rays backwards. Converging Lens Real Object Side (+) Real Image Side (+) Virtual Object Side (-) Virtual Image Side (-) Real Image Side (+) Real Object Side (+) Virtual Object Side (-)

Ray tracing with lenses: Diverging Lens X X f f 1 st : Draw a line through the middle lens 2 nd :Draw a line parallel to axis and make its projection pass through the focal point X X f f

Len’s makers equation: here, i is the image distance, o is the object distance and f is the focal length. NOTE: If, i, o are on their VIRTUAL SIDES they will be negative. Let’s look at an example: An object 3 cm high is placed 15 cm in front of a converging lens of 10 cm focal length. Where is the image located? Since this is a converging lens and the object is outside the focal length we know that the image formed will be a REAL IMAGE, so is will be positive. So we use the len’s maker’s equation to solve for i.