Convex Mirrors. Ray Diagram for Convex Mirror

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1 Convex Mirrors Center of curvature and focal point both located behind mirror The image for a convex mirror is always virtual and upright compared to the object A convex mirror will reflect a set of parallel rays in all directions; conversely, it will also take light from all directions and reflect it in one direction Used for security in stores, and is also the kind of mirror used on the passenger side of many cars Ray Diagram for Convex Mirror Sign convention remains same REMEMBER focal point, f and radius of curvature, C will be negative (behind mirror)

2 Sign Convention for Spherical Mirrors The sign conventions for the given quantities in the mirror equation and magnification equations are as follows: fis + if the mirror is a concave mirror (radius of curvature = 2f, also positive) fis - if the mirror is a convex mirror (radius of curvature = 2f, also negative) d i is + if the image is a real image and located on the object's side of the mirror. d i is - if the image is a virtual image and located behind the mirror. h i is + if the image is an upright image (and therefore, also virtual) h i is - if the image an inverted image (and therefore, also real) M is + if the image is enlarged M is - if the image is reduced

3 Example A convex spherical mirror with radius of curvature of 10 cm produces a virtual image one third the size of the object. Where is the object located?

4 Images formed by Refraction Refraction is the bending of a wave when it enters a medium where it's speed is different. Refraction is responsible for image formation by lenses and the eye. In this case the light from the object passes through the lens and is bent, forming an image on the other side of the lens which is magnified and inverted.

5 Images formed by Refraction Example: Looking at an object in a pool, the object will appear closer than it actually is. This is due to the fact that light is bent when passing from water to air, as indicated below. Note that since air is less dense than water, the light bends away from the normal as it emerges. Your eye doesn't know that the light has been refracted when it comes from water into air, and so thinks that it has originated from a point closer to the surface.

6 Lenses (Remember - light passes through lenses; lenses can reflect or refract light) Double-convex lens Is converging lens Double-concave lens Is diverging lens A converging lensis a lens that converges rays of light that are traveling parallel to its principal axis. (Relatively thick across their middle and thin at their upper and lower edges.) A diverging lensis a lens that diverges rays of light that are traveling parallel to its principal axis. (Relatively thin across their middle and thick at their upper and lower edges.)

7 Refraction and Converging Lenses If the path of several light rays through a lens is traced, each of these light rays will intersect at a point upon refraction through the lens. Diagram below shows several incident rays emanating from an object Each incident ray will refract through the lens The refracted rays are intersecting is the image location (converging). Converging lenses can produce both real and virtual images Here, the image is a real image since the light rays are actually passing through the image location

8 Ray Diagrams for Converging Lenses Three rules of refraction for a double convex (converging) lens: Any incident ray traveling parallel to the principal axis of a converging lens will refract through the lens and travel through the focal point on the opposite side of the lens. Any incident ray traveling through the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis. An incident ray that passes through the center of the lens will in effect continue in the same direction that it had when it entered the lens.

9 Ray Diagrams for Converging Lenses

10 Refraction and Diverging Lenses Diverging lens create virtual images since the refracted rays do not actually converge to a point The image location is located on the object's side of the lens where the refracted rays would intersect if extended backwards The location where the refracted rays are intersecting is the image location. Since refracted light rays do not actually exist at the image location, the image is said to be a virtual image.

11 Ray diagrams and Diverging Lenses Three simple rules of refraction for double concave (diverging) lenses: Any incident ray traveling parallel to the principal axis of a diverging lens will refract through the lens and travel in line with the focal point (i.e., in a direction such that its extension will pass through the focal point). Any incident ray traveling towards the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis. An incident ray that passes through the center of the lens will in affect continue in the same direction that it had when it entered the lens.

12 Ray diagrams and Diverging Lenses The diagrams above show that in each case, the image is located on the object' side of the lens a virtual image an upright image reduced in size (i.e., smaller than the object) Unlike converging lenses, diverging lenses always produce images that share these characteristics.

13 Refraction from Plane Surfaces Rays originating at the object location are refracted at the spherical surface and converge at the image point. n 1 index of refraction for 1 st medium h o height of object d o distance from lens surface to object R radius of curvature n 2 index of refraction for 2nd medium h i height of image d i distance from lens surface to image Relating n and d(derivation combines Snell s law & geometry): n 1 /d o + n 2 /d i = (n 2 n 1 )/R Magnification: M = h i /h o = - n 2 d i /n 1 d o For plane surface (R = ): n 1 /d o = - n 2 /d i

14 Sign Convention for Refracting Surfaces The sign conventions for the given quantities R is + if center of curvature is in back of the surface R is - if center of curvature is in front of the surface d o is + if the object is in front of the surface (real object) d o is - if the object is in back of the surface (virtual object) d i is + if the image is in back of the surface (real image) d i is - if the image in front of the surface (virtual image) Sign convention for spherical refracting surfaces is the same as for mirrors, recognizing the changes in sides of the surface for real and virtual images.

15 Example A goldfish is swimming in water inside a spherical plastic bowl of index of refraction If the goldfish is 10 cm from the wall of the 15-cm-radius bowl, where does the goldfish appear to an observer outside the bowl?

16 Example A diverging lens is used to form a virtual image of an object. The object is 80 cm to the left of the les and the image is 40 cm to the left of the lens. Determine the focal length of the lens.