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Physics 6CGeometric OpticsMirrors and Thin LensesPrepared by Vince ZacconeFor Campus Learning Assistance Services at UCSB

We have already learned the basics of Reflection and Refraction.Reflection - angle of incidence = angle of reflectionRefraction - light bends toward the normal according to Snells LawNow we apply those concepts to some simple types of mirrors and lenses.Prepared by Vince ZacconeFor Campus Learning Assistance Services at UCSB

We have already learned the basics of Reflection and Refraction:Reflection - angle of incidence = angle of reflectionRefraction - light bends toward the normal according to Snells LawNow we apply those concepts to some simple types of mirrors and lenses.Flat MirrorThis is the simplest mirror a flat reflecting surface. The light rays bounce off and you see an image that seems to be behind the mirror. This is called a VIRTUAL IMAGE because the light rays do not actually travel behind the mirror. The image will appear reversed, but will be the same size and the same distance from the mirror. A typical light ray entering the eye of the viewer is shown.The object distance is labeled S and the image distance is labeled S.Virtual ImageSReal ObjectPrepared by Vince ZacconeFor Campus Learning Assistance Services at UCSB

Spherical MirrorsFor curved mirrors we will assume that the shape is spherical (think of a big shiny ball, and slice off any piece of that theres your spherical mirror). This will make our math relatively simple, with only a couple of formulas. The hard part will be to get the negative signs correct.The radius of curvature describes the shape of the mirror. This is the same as the radius of the big shiny ball that the mirror was cut from.We will have two types of mirrors, depending on which direction they curve:CONCAVE mirrors curve toward you, and have POSITIVE R (like the inside of the sphere).CONVEX mirrors curve away from you, and have NEGATIVE R (think of the outside of the ball).There is a point called the FOCAL POINT which is halfway between the mirror and the center.Concave Mirror R is positiveConvex Mirror R is negativePrepared by Vince ZacconeFor Campus Learning Assistance Services at UCSBShiny sideShiny side

We will learn 2 techniques for dealing with mirrors (and lenses): Graphical draw the light rays and the image is at their intersection. Formula use a couple of formulas to locate and describe an image.First the Graphical Method:For a spherical mirror there are 3 basic rays that you can draw:Any ray that goes through the CENTER of the circle reflects directly back to the light source.Any ray that goes through the FOCAL POINT is reflected back PARALLEL to the optical axis.Any ray that starts parallel to the optical axis is reflected back through the focal point. (opposite of 2)Prepared by Vince ZacconeFor Campus Learning Assistance Services at UCSB

Optical AxisFocal PointRay 1 through the centerPrepared by Vince ZacconeFor Campus Learning Assistance Services at UCSBWe will learn 2 techniques for dealing with mirrors (and lenses): Graphical draw the light rays and the image is at their intersection. Formula use a couple of formulas to locate and describe an image.First the Graphical Method:For a spherical mirror there are 3 basic rays that you can draw:Any ray that goes through the CENTER of the circle reflects directly back to the light source.Any ray that goes through the FOCAL POINT is reflected back PARALLEL to the optical axis.Any ray that starts parallel to the optical axis is reflected back through the focal point. (opposite of 2)

Optical AxisFocal PointRay 1 through the centerRay 1 reflects directly back Prepared by Vince ZacconeFor Campus Learning Assistance Services at UCSBWe will learn 2 techniques for dealing with mirrors (and lenses): Graphical draw the light rays and the image is at their intersection. Formula use a couple of formulas to locate and describe an image.First the Graphical Method:For a spherical mirror there are 3 basic rays that you can draw:Any ray that goes through the CENTER of the circle reflects directly back to the light source.Any ray that goes through the FOCAL POINT is reflected back PARALLEL to the optical axis.Any ray that starts parallel to the optical axis is reflected back through the focal point. (opposite of 2)

Optical AxisFocal PointRay 2 through the focal pointPrepared by Vince ZacconeFor Campus Learning Assistance Services at UCSBWe will learn 2 techniques for dealing with mirrors (and lenses): Graphical draw the light rays and the image is at their intersection. Formula use a couple of formulas to locate and describe an image.First the Graphical Method:For a spherical mirror there are 3 basic rays that you can draw:Any ray that goes through the CENTER of the circle reflects directly back to the light source.Any ray that goes through the FOCAL POINT is reflected back PARALLEL to the optical axis.Any ray that starts parallel to the optical axis is reflected back through the focal point. (opposite of 2)

Optical AxisFocal PointRay 2 through the focal pointRay 2 reflects parallel to axisPrepared by Vince ZacconeFor Campus Learning Assistance Services at UCSBWe will learn 2 techniques for dealing with mirrors (and lenses): Graphical draw the light rays and the image is at their intersection. Formula use a couple of formulas to locate and describe an image.First the Graphical Method:For a spherical mirror there are 3 basic rays that you can draw:Any ray that goes through the CENTER of the circle reflects directly back to the light source.Any ray that goes through the FOCAL POINT is reflected back PARALLEL to the optical axis.Any ray that starts parallel to the optical axis is reflected back through the focal point. (opposite of 2)

Optical AxisFocal PointRay 3 comes in parallel to axisPrepared by Vince ZacconeFor Campus Learning Assistance Services at UCSBWe will learn 2 techniques for dealing with mirrors (and lenses): Graphical draw the light rays and the image is at their intersection. Formula use a couple of formulas to locate and describe an image.First the Graphical Method:For a spherical mirror there are 3 basic rays that you can draw:Any ray that goes through the CENTER of the circle reflects directly back to the light source.Any ray that goes through the FOCAL POINT is reflected back PARALLEL to the optical axis.Any ray that starts parallel to the optical axis is reflected back through the focal point. (opposite of 2)

Optical AxisFocal PointRay 3 reflects through focal pointRay 3 comes in parallel to axisPrepared by Vince ZacconeFor Campus Learning Assistance Services at UCSBWe will learn 2 techniques for dealing with mirrors (and lenses): Graphical draw the light rays and the image is at their intersection. Formula use a couple of formulas to locate and describe an image.First the Graphical Method:For a spherical mirror there are 3 basic rays that you can draw:Any ray that goes through the CENTER of the circle reflects directly back to the light source.Any ray that goes through the FOCAL POINT is reflected back PARALLEL to the optical axis.Any ray that starts parallel to the optical axis is reflected back through the focal point. (opposite of 2)

Optical AxisObject132ImagePrepared by Vince ZacconeFor Campus Learning Assistance Services at UCSBWe will learn 2 techniques for dealing with mirrors (and lenses): Graphical draw the light rays and the image is at their intersection. Formula use a couple of formulas to locate and describe an image.First the Graphical Method:For a spherical mirror there are 3 basic rays that you can draw:Any ray that goes through the CENTER of the circle reflects directly back to the light source.Any ray that goes through the FOCAL POINT is reflected back PARALLEL to the optical axis.Any ray that starts parallel to the optical axis is reflected back through the focal point. (opposite of 2)All 3 rays shown with the image at their intersection

Example using the Formula Method:A concave makeup mirror with radius of curvature 0.5m is held 0.2m from a womans face.Where is her image and how large is it?Prepared by Vince ZacconeFor Campus Learning Assistance Services at UCSB

Example using the Formula Method:A concave makeup mirror with radius of curvature 0.5m is held 0.2m from a womans face.Where is her image and how large is it?Before we answer this lets look at a few basic formulas for spherical mirrors.1) The focal length is half the radius.Prepared by Vince ZacconeFor Campus Learning Assistance Services at UCSBRemember the sign convention if the mirror is concave R is positive. If convex, R is negative.

Example using the Formula Method:A concave makeup mirror with radius of curvature 0.5m is held 0.2m from a womans face.Where is her image and how large is it?Before we answer this lets look at a few basic formulas for spherical mirrors.1) The focal length is half the radius.2) This formula relates the object (S) and image (S) positions to the focal length (f) of the mirror.Prepared by Vince ZacconeFor Campus Learning Assistance Services at UCSBHere S is always positive for mirrors, and S is positive if the image is on the same side as the object (a REAL image).To remember this, just follow the light a real (positive) image will have light rays passing through it.Remember the sign convention if the mirror is concave R is positive. If convex, R is negative.

Example using the Formula Method:A concave makeup mirror with radius of curvature 0.5m is held 0.2m from a womans face.Where is her image and how large is it?Before we answer this lets look at a few basic formulas for spherical mirrors.1) The focal length is half the radius.2) This formula relates the object (S) and image (S) positions