With Curved Mirrors Forming Images Created by Derek J. Wells. Under the expressed written consent of Derek J. Wells in accordance with the rules and by-laws of Derek J. Wells. All events depicted here are fictional. Any similarity to real life situations are merely coincidental.

Types of Mirrors The everyday flat type of mirror is called a “plane mirror”. All light traveling straight towards this mirror reflects right back at you. As such, you always get an image that is an exact duplicate of you. Remember, MIRRORS REFLECT LIGHT, so it bounces off them. This may seem silly in that we already know that, but as we talk of more optical instruments its something you should keep in mind. Curved mirrors are not flat and therefore light reflects differently off them making different types of images. There are two types of curved mirrors A concave mirror. And A convex mirror This mirror has a concave shape when looking at it from the left side. This mirror has a convex shape when looking at it from the left side This mirror looks like a “cave” if you were walking into it from the left side.

The concave mirror is also called a converging mirror because it causes horizontal light rays to converge (come together) when they reflect off the mirror The convex mirror is also called a diverging mirror because it causes horizontal light rays to diverge (move apart) when they reflect off the mirror

Terminology Curved mirrors are approximated to have a circular shape. We can make a curved mirror by cutting part of mirrored circle out. The mirror was cut from a circle.

Terminology The center of the circle that the mirror is part of is point C. Point C is called: C= Center of Curvature C R The radius of the circle that the mirror is part of is distance R Distance R is called: R= Radius of Curvature

Terminology Principle Axis = The horizontal line drawn through the center C C f f f = Focal point (of convex mirror) = the point at which all reflected rays APPEAR to come from when they reflect f = Focal point (of a concave mirror) = the point through which all reflected rays bouncing off the mirror CONVERGE The focal point(f) is 1/2 of the distance to the center of curvature point (C) f = R / 2

Terminology Distance object is placed from the mirror Also ho = object height hi = image height An object placed near a mirror The image of the object that is produced by the mirror f C di Distance image is formed from the mirror Front Side of Mirror (the real side) Back Side of Mirror (the virtual side) When images are formed on the front side of the mirror they are real images. Real images can be projected onto a screen. When images are formed on the back side of the mirror they are virtual images.

Concave mirrors can form any types of these images: Curved Mirrors Concave mirrors can form any types of these images: - real or virtual - smaller, same size, or larger - real images are ALWAYS inverted or upside down Convex mirrors can only form one type of image ALWAYS: - virtual - smaller - upright Important - when using a convex mirror the focal point (f) must be negative (-) because it is behind the mirror

Ray Diagrams (for concave mirrors) The FIRST incident light ray we draw goes horizontally straight towards the mirror (Parallel) C f This light ray reflects back and passes through the focal point (Focal)

Ray Diagrams (for concave mirrors) The second incident light ray we draw goes through the focal point before it hits the mirror C f This light ray reflects back parallel to the optical axis

L = location of image compared to actual object Putting it all together. Draw both rays, and the point where they intersect or converge represents the point where the tip of the image will be formed BEYOND C... Image C f Describe the image (LOST): L = Closer O = Inverted S = Smaller T = Real L = location of image compared to actual object O = Orientation of Image S = Size of Image T = Type of Image

Special Examples 1- When the object is located exactly on (f) the rays will not intersect anywhere and there will be no image 2- When the object is placed right on C, the REAL image is inverted and the same size At C... Image C f Describe the image: L = same O = inverted S = same T = real

Inside F... Special Examples 3 - When the object is placed in front of f... We extend the reflected rays back behind the mirror to see where they appear to come from. This is the image point. Inside F... Image Notice that these rays do not intersect anywhere over here C f Describe the image: L = farther O = upright S = Larger T = Virtual

Ray Diagrams (for convex mirrors) The nice thing about Convex mirrors is that the ray diagrams are ALWAYS, ALWAYS the same. They are slightly different then the concave mirrors however and you should be careful to notice the differences. In this type of mirror, you always have to extend the reflected rays back behind to find the image For example... f C

Parallel, then focal Ray Diagrams (for convex mirrors) C f The first light ray is: Parallel, then focal This light ray reflects back AS IF it came from point “f”

Focal, then parallel Ray Diagrams (for convex mirrors) C f The second light ray is: Focal, then parallel This light ray reflects back horizontally (parallel)

Ray Diagrams (for convex mirrors) Put them all together and extend the reflected rays behind the mirror to find the object Notice that these rays do not intersect anywhere over here We extend the reflected rays back behind the mirror to see where they appear to come from. This is the image point. Image f C Describe the image: L = closer O = upright S = smaller T = Virtual