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Dorothea Lange 1936

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HomeworkChapter 3

P3,P5,P6,P9,P10,P11,PH4,PM3

• Only 67 of 88 students handed in HW#1.• Your grades are on WebCT.• The solutions are posted on the course website.

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Refraction Review rays bend toward the normal going from

low index to high index (air to glass)

rays bend away from normal going fromhigh index to low index (glass to air)

the angle of incidence where the angle ofrefraction = 90 deg. is the critical angle- above this everything is total internal reflected

the index of refraction depends on wavelength different colors refract by different angles - dispersion

dispersion is responsible for the rainbow4

Geometrical Optics

How mirrors and lenses work…

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Clicker QuestionA fish swims below the surface.An observer looking at the fishfrom straight above, sees the fishat:

1 ) a greater depth than it really is.

2) The same depth.

3) A shallower depth than it really is.

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Clicker QuestionA fish swims below the surface.An observer looking at the fishfrom straight above, sees the fishat:

3) A shallower depth than it really is.

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Images

• Real Images– Image is formed by intersecting rays that

came from source• Virtual Images

– Image is formed by rays that appear tointersect at the image

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Real Image

object

image

More on lenses later…

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Virtual Image

object

image

mirror

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Plane Mirror Image

object

image

mirror

• virtual image• upright (non-inverted)• same size as object (magnification =1)• same distance from mirror as object

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Spherical Mirrors

• reflector in the shape of part of asphere

Convex Concave

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Convex mirror

CF

O

C - centerF - focal point

Ray Rule I - all rays parallel to the axis arereflected so that they appear to be comingfrom the focal point F.

Focal length ff = OF = 1/2 OC

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Convex mirror

CF

O

C - centerF - focal point

Focal length ff = OF = 1/2 OC

Ray Rule II - all rays (when extended) aimedat C are reflected back on themselves

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Convex mirror

CF

O

C - centerF - focal point

Focal length ff = OF = 1/2 OC

Ray Rule III - all rays (when extended) aimedat F are reflected back parallel to the axis

This is just Rule I reversed

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Finding the image

CF

O

- draw ray from object point Q towards C- draw ray from Q parallel to axis; extend from mirror surface to F- where the extended rays intersect is Q’

Q

P

Q’

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Image formation

• http://www.phys.hawaii.edu/~teb/optics/java/dmirr/index.html

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Image from a convex mirror

http://www.microscopy.fsu.edu/primer/java/mirrors/convex.html

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Properties of the image• It is a virtual image• It is an upright (or erect) image.• It is closer to the mirror than the real

object• The image is smaller than the real

object.• Applications: store and car

– (allows to see wider angles)

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Parallel Light From Faraway

• All rays are nearly parallel.• Rays parallel to each other are imaged

on the focal plane.• The image comes from a ray passing

through the center of the mirror, OR aray going through the focal point.

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Anamorphic ArtM. C. Escher

Hand withReflecting Globe

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21Hans Holbein - The Ambassadors