Presentation on theme: "Notation for Mirrors and Lenses"— Presentation transcript:
1 Notation for Mirrors and Lenses The object distance is the distance from the object to the mirror or lensDenoted by pThe image distance is the distance from the image to the mirror or lensDenoted by qThe lateral magnification of the mirror or lens is the ratio of the image height to the object heightDenoted by M
2 ImagesImages are always located by extending diverging rays back to a point at which they intersectImages are located either at a point from which the rays of light actually diverge or at a point from which they appear to diverge
3 Types of ImagesA real image is formed when light rays pass through and diverge from the image pointReal images can be displayed on screensA virtual image is formed when light rays do not pass through the image point but only appear to diverge from that pointVirtual images cannot be displayed on screens
4 Images Formed by Flat Mirrors Simplest possible mirrorLight rays leave the source and are reflected from the mirrorPoint I is called the image of the object at point OThe image is virtual
5 Images Formed by Flat Mirrors One ray starts at point P, travels to Q and reflects back on itselfAnother ray follows the path PR and reflects according to the law of reflectionThe triangles PQR and P’QR are congruent
6 Lateral Magnification Lateral magnification, M, is defined asThis is the general magnification for any type of mirrorIt is also valid for images formed by lensesMagnification does not always mean bigger, the size can either increase or decreaseM less than 1 -> image size decreasedM greater than 1 -> image size increased
7 Reversals in a Flat Mirror A flat mirror produces an image that has an apparent left-right reversalFor example, if you raise your right hand the image you see raises its left hand
8 Spherical MirrorsA spherical mirror has the shape of a section of a sphereThe mirror focuses incoming parallel rays to a pointA concave spherical mirror has the silvered surface of the mirror on the inner, or concave, side of the curveA convex spherical mirror has the silvered surface of the mirror on the outer, or convex, side of the curve
13 Ray Tracing Parallel ray hit the mirror and heads to the focus Ray through focus hits the mirror and comes off parallelRay through center of curvature returns to center of curvature
14 Ray TracingFCParallel ray hits the mirror and reflects as if it started at the focusRay heading to the focus hits the mirror and comes off parallelRay heading to the center of curvature returns along the same path
15 MagnificationGain is a betterdescription since Mmight be < 1Or:
20 Flat Refracting Surfaces If a refracting surface is flat, then R is infiniteThen q = -(n2 / n1)pThe image formed by a flat refracting surface is on the same side of the surface as the objectA virtual image is formed
21 Locating the Image Formed by a Lens The lens has an index of refraction n and two spherical surfaces with radii of R1 and R2R1 is the radius of curvature of the lens surface that the light of the object reaches firstR2 is the radius of curvature of the other surfaceThe object is placed at point O at a distance of p1 in front of the first surfaceSmall!!
22 Lens Makers’ EquationThe focal length of a thin lens is the image distance that corresponds to an infinite object distanceThis is the same as for a mirrorThe lens makers’ equation is
29 ExampleA 2 cm tall object is placed 30 cm in front of a diverging lens with a focal length of –20 cm. Find the location of the image, its classification, the size of the image, and the magnification. Construct a ray diagram.
31 Multiple Thin Lenses Find the image distance of the first lens. Use the image of the first lens as the object of the second lens.Find the new object distance by correcting with the separation of the lenses.Find the image of the second lens.Transverse Magnification is the product of the magnifications of the individual lenses
32 ExampleFind the location and magnification of the final image formed
33 9. A spherical convex mirror has a radius of curvature with a magnitude of 40.0 cm. Determine the position of the virtual image and the magnification for object distances of (a) 30.0 cm and (b) 60.0 cm. (c) Are the images upright or inverted?11. A concave mirror has a radius of curvature of 60.0 cm. Calculate the image position and magnification of an object placed in front of the mirror at distances of (a) 90.0 cm and (b) 20.0 cm. (c) Draw ray diagrams to obtain the image characteristics in each case.12. A concave mirror has a focal length of 40.0 cm. Determine the object position for which the resulting image is upright and four times the size of the object.
34 29. The left face of a biconvex lens has a radius of curvature of magnitude 12.0 cm, and the right face has a radius of curvature of magnitude 18.0 cm. The index of refraction of the glass is (a) Calculate the focal length of the lens. (b) What If? Calculate the focal length the lens has after is turned around to interchange the radii of curvature of the two faces.31. A thin lens has a focal length of 25.0 cm. Locate and describe the image when the object is placed (a) 26.0 cm and (b) 24.0 cm in front of the lens.34. A person looks at a gem with a jeweler’s loupe—a converging lens that has a focal length of 12.5 cm. The loupe forms a virtual image 30.0 cm from the lens. (a) Determine the magnification. Is the image upright or inverted? (b) Construct a ray diagram for this arrangement.