Lenses and Mirrors

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Lenses and Mirrors
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• How does light interact with pinholes?
• How does light interact with lenses?
• Refraction
• How does light interact with mirrors?
• Reflection
• We can use the photon model.

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Pinholes

• A pinhole can be used to form an image.

Light rays from point source
screen
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Image formation with a Pinhole camera
Light source
Dark room Camera
do distance from object to pinhole di
distance from pinhole to image ho
height of object hi height of image
Image is fuzzy if pinhole is larger Image is
sharper if pinhole is smaller Image is dimmer is
pinhole is smaller
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Mirrors

• Flat
• Concave
• Convex

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The Law of Reflection

• For reflection the incident angle qi equals the
  reflected angle qr
• qi qr

The angles are measured relative to the normal,
shown here as a dotted line.
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Forming Images with a Plane Mirror

• A mirror is an object that reflects light. A
  plane mirror is simply a flat mirror.
• Consider an object placed at point P in front of
  a plane mirror. An image will be formed at point
  P behind the mirror.

do distance from object to mirror di distance
from image to mirror ho height of object hi
height of image
hi
ho
do
di
For a plane mirror do -di and ho hi
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Images

• An image is formed at the point where the rays of
  light leaving a single point on an object either
  actually intersect or where they appear to
  originate from.
• If the light rays actually do intersect, then the
  image is a real image. If the light only appears
  to be coming from a point, but is not physically
  there, then the image is a virtual image.
• We define the magnification, m, of an image to be

If m is negative, the image is inverted (upside
down).
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Images

• An image is formed at the point where the rays of
  light leaving a single point on an object either
  actually intersect or where they appear to
  originate from.

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Images

• If the light rays actually do intersect, then the
  image is a real image. If the light only appears
  to be coming from a point, but is not physically
  there, then the image is a virtual image.

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Images

• We define the magnification, m, of an image to
  be

If m is negative, the image is inverted (upside
down).
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Spherical Mirrors

• A spherical mirror has a surface shape with
  radius of curvature R. There are two types of
  spherical mirrors concave and convex.

concave
convex
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Focal Point
When parallel rays (e.g. rays from a distance
source) are incident upon a spherical mirror,
the reflected rays intersect at the focal point
F, a distance R/2 from the mirror.
For a concave mirror, the focal point is in front
of the mirror (real).
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Focal Point
For a convex mirror, the focal point is behind
the mirror (virtual).
The incident rays diverge from the convex
mirror, but they trace back to the focal point F.
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Focal Length
The focal length f is the distance from the
surface of the mirror to the focal point. It can
be shown that the focal length is half the radius
of curvature of the mirror. Sign Convention the
focal length is negative if the focal point is
behind the mirror. For a concave mirror, f
½R For a convex mirror, f ?½R (R always )
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Ray Tracing
It is sufficient to use three principal rays to
determine image location.
The parallel ray (P ray) reflects through the
focal point. The focal ray (F ray) reflects
parallel to the axis, and the center-of-curvature
ray (C ray) reflects back along its incoming path.
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Ray Tracing Examples
Put film here for Sharp image.
concave
convex
Virtual image
Real image
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Lenses

• Concave
• Convex
• Refraction

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Reflection and Refraction

• When a light ray travels from one medium to
  another, part of the incident light is reflected
  and part of the light is transmitted at the
  boundary between the two media.
• The transmitted part is said to be refracted in
  the second medium.

incident ray
reflected ray
refracted ray
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(No Transcript)
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Red Light
Red Light
Red Light
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Lenses
Light is reflected from a mirror. Light is
refracted through a lens.
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Focal Point
The focal point of a lens is the place where
parallel rays incident upon the lens converge.
diverging lens
converging lens
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Ray Tracing for Lenses
Just as for mirrors we use three easy rays to
find the image from a lens.
P ray travels parallel to the principal axis
until lens, it refracts to pass through the focal
point on the far side of the lens. The F ray
passes through the focal point on the near side
of the lens, leaves parallel to the principal
axis. The M ray passes through the middle of the
lens with no deflection.
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Focal Length
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• http//www.physics.odu.edu/hyde/Teaching/Spring04/
  Lectures/318,1,Chapter 26 Geometrical Optics