Optics

What is the mirror equation?

f

• concave/converging = (+)

• convex/diverging = (-)

i

• real = (+)

• virtual = (-)

o

• always (+)

(+) > 0

(-) < 0

What is the magnification equation?

ho = height of object

• always (+)

hi = height of image

• upright (+) → i (-)

• inverted (-) → i (+)

M

• upright (+)

• inverted (-)

|M|

• larger (>1)

• smaller (<1)

• same size (=1)

What is the law of reflection?

• surface normal is perpendicular to surface from which light reflects

• $\theta i$ = incoming angle

• $\theta r$ = angle of reflection

• yi and yr

Draw the diagram for concave mirrors

• “inside of a spoon”

Bottom diagram

• object away from focal point and mirror

• real, inverted, small

Top diagram

• object between focal point and mirror

• virtual, upright, enlarged

Main difference

• for the bottom diagram, rays don’t physically intersect

• have to backtrace to make them intersect (so they’re virtual)

Real vs virtual images

Real

• reflected rays physically meet

• formed on same side of mirror as object

• inverted

• concave mirrors

Virtual

• reflected rays don’t physically meet

• formed on opposite side of mirror than object

• upright

• Sometimes concave, always convex

Concave mirrors can make _____ images, while convex mirrors can make _____ images

either real or virtual

only virtual

Draw the diagram for convex mirrors

• “outside of spoon”

• ALWAYS virtual, upright, smaller than object

Define each of the following:

• C

• R

• f

What two equations can we derive from this information?

• C = center of curvature

• R = distance from center to mirror (aka “radius of curvature”)

• f = point at which rays meet

• R/2 = distance from focal point to mirror

Equations

• R = 2f

• f = R/2

Equations for composite multiple mirrors

• M(tot) = M1 x M2 x … M(final)

• M(tot) = (-i2/o2)(-i1/o1) = M1 x M2

Complete the summary table for both types of mirrors and lens

• use i, o, f, and M

• concave → converging

• convex → diverging

What can be said about this equation?

How do o2 and i1 relate?

What are some M equations/facts we should know?

What is the most important thing to know about this system: 1 lens and 2 objects?

1 lens = 1 focal point

How to distinguish between mirrors and lens given object, focal point, or image?

How to distinguish between converging/concave and diverging/convex?

can use o and f to narrow down possibilities

If an image moves closer/farther from an mirror, how does the object move?

note: concave mirror can produce both real and virtual images

You are asked about the distance an object has moved? How can we solve this?

o2 - o1