Mirrors and Lenses
- Images
- Real
- can be formed on a screen
- rays appear to converge to a point
- Virtual
- image appears "in" the mirror
- rays appear to diverge from a point
- Plane Mirrors
- p = object distance
- i = image distance
- Using ray tracing
- Concave Mirrors
- h = height of the object
- h' = height of the image
- comparing similar triangles
- Equating the two expressions for h'/h
- Dividing both sides of the last equation by Rpi
- Convex Mirrors
- We will get the same result for a convex
mirror is we follow the sign convention for
mirrors.
- Sign Convention (Mirrors)
- p
- + object is located in front of mirror (real)
- - object is located behind mirror (virtual)
- i
- + image is located in front of the mirror (real)
- - image is located behind the mirror (virtual)
- R
- + center of curvature located in front of mirror (concave)
- - center of curvature located behind the mirror (convex)
- Refracting Surfaces
- Apply Snell's Law to the surface
- Use small angle approximation
- Also by geometry the following relationships hold
\
- Substituting the above expressions into our small angle approximation form for Snell's
Law
- and replacing a, b and
g by the form we obtained using the small angle
approximation
- Canceling the d from all terms gives
- Sign Convention (Refracting Surfaces)
- p
- + object is located in front of surface (real)
- - object is located behind surface (virtual)
- i
- + image is located behind the surface (real)
- - image is located in front of the mirror (virtual)
- R
- + center of curvature located behind the surface (convex)
- - center of curvature located in front of the surface (concave)
- Thin Lenses
- Converging Lens
- Diverging Lens
- Sign Convention (Lens)
- p
- + object is located in front of lens (real)
- - object is located behind lens (virtual)
- i
- + image is located behind the lens (real)
- - image is located in front of the lens (virtual)
- f
- + converging lens (center thicker than ends)
- - diverging lens (center thinner than ends)
