Mirrors and Lenses

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Chapter 23

• Mirrors and Lenses

Conceptual questions 4,5,10,14,15,17 Quick
Quizzes 1,2,4,6 Problems 17,44,53,61
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Types of Images for Mirrors and Lenses

• A real image is one in which light actually
  passes through the image point
• Real images can be displayed on screens
• A virtual image is one in which the light does
  not pass through the image point
• Virtual images cannot be displayed on screens

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Flat Mirror

• The object distance is the distance from the
  object to the mirror or lens
• Denoted by p
• The image distance is the distance from the image
  to the mirror or lens
• Denoted by q
• The lateral magnification of the mirror or lens
  is the ratio of the image height to the object
  height
• Denoted by M

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QUICK QUIZ 23.1
In the overhead view of the figure below, the
image of the stone seen by observer 1 is at C.
Where does observer 2 see the imageat A, at B,
at C, at D, at E, or not at all?
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Day and Night Settings on Auto Mirrors
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Concave Mirror

• The mirror has a radius of curvature of R
• Its center of curvature is the point C
• Point V is the center of the spherical segment
• A line drawn from C to V is called the principle
  axis of the mirror

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Image Formed by a Concave Mirror

• Geometry shows the relationship between the image
  and object distance is
• Magnification is

• h is negative when the image is inverted with
  respect to the object

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Focal Length Shown by Parallel Rays
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Focal Length

• Focal length, the distance between the focal
  point and the mirror, is half the radius
• The mirror equation can be expressed as

f R / 2
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Convex Mirrors

• A convex mirror is also called a diverging mirror

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Ray Diagram

• Ray 1 is drawn parallel to the principle axis and
  is reflected back through the focal point, F
• Ray 2 is drawn through the focal point and is
  reflected parallel to the principle axis
• Ray 3 is drawn through the center of curvature
  and is reflected back on itself

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Ray Diagram for Concave Mirror, p gt R
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Draw a ray diagram fora. a convex mirrorb. a
concave mirror with the object at a distance pgtR
Based on conceptual question 17
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Ray Diagram for a Convex Mirror
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Ray Diagram for a Concave Mirror, p lt f
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True or false?
(a) The image of an object placed in front of a
concave mirror is always upright. (b) The height
of the image of an object placed in front of a
concave mirror must be smaller than or equal to
the height of the object. (c) The image of an
object placed in front of a convex mirror is
always upright and smaller than the object.
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Problem 17

• A child holds a candy bar 10.0 cm in front of a
  convex mirror and notices that the image is only
  one-half the size of the candy bar. What is the
  radius of curvature of the mirror?

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Images Formed by Refraction

• When n2 gt n1,
• Object distance, image distance and radius of
  curvature are related by the equation
• Real images are formed on the side opposite from
  the object
• Sign conventions Table 23.2

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Sign convention for refracting surfaces
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Flat Refracting Surface

• The image and the object are on the same side of
  the surface. The image is virtual

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QUICK QUIZ 23.2

• A person spear fishing from a boat sees a fish
  located 3 m from the boat at an apparent depth of
  1 m. To spear the fish, should the person aim
• at,
• (b) above, or
• (c) below the image of the fish?

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Problem 53

• A parallel beam of light enters a glass
  hemisphere perpendicular to the flat face, as
  shown in Figure P23.53. The radius is R 6.00
  cm, and the index of refraction is n 1.560.
  Determine the point at which the beam is focused.
  (Assume paraxial rays that is, all rays are
  located close to the principal axis.)

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Conceptual question

• 10. Why does a clear stream appear to be
  shallower than it actually is?

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Atmospheric Refraction and Mirages

• A mirage can be observed when the air above the
  ground is warmer than the air at higher
  elevations
• The rays in path B are directed toward the ground
  and then bent by refraction
• The observer sees both an upright and an inverted
  image

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Thin Lens Shapes

• These are examples of converging lenses
• They have positive focal lengths
• They are thickest in the middle

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Thin Diverging Lenses

• These are examples of diverging lenses
• They have negative focal lengths
• They are thickest at the edges

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Lens Equations

• The geometric derivation of the equations is very
  similar to that of mirrors

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Sign Conventions for Thin Lenses
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The Lens Makers formulae
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Ray Diagrams for Thin Lenses

• The first ray is drawn parallel to the first
  principle axis and then passes through (or
  appears to come from) one of the focal lengths
• The second ray is drawn through the center of the
  lens and continues in a straight line
• The third ray is drawn from the other focal
  point and emerges from the lens parallel to the
  principle axis

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Ray Diagram for Converging Lens, p gt f

• The image is real
• The image is inverted

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Ray Diagram for Converging Lens, p lt f

• The image is virtual
• The image is upright

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Ray Diagram for Diverging Lens

• The image is virtual
• The image is upright

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Conceptual questions

• 5. You are taking a picture of yourself with a
  camera that uses an ultrasonic range finder to
  measure the distance to the object. When you
  take a picture of yourself in a mirror with this
  camera, your image is out of focus. Why?
• 14. Lenses used in sunglasses whether converging
  or diverging, are always designed such that the
  middle of the lens curves away from the eye. Why?

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QUICK QUIZ 23.4
A plastic sandwich bag filled with water can act
as a crude converging lens in air. If the bag is
filled with air and placed under water, is the
effective lens (a) converging or (b) diverging?
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QUICK QUIZ 23.6
An object is placed to the left of a converging
lens. Which of the following statements are true
and which are false? (a) The image is always to
the right of the lens. (b) The image can be
upright or inverted. (c) The image is always
smaller or the same size as the object.
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Combination of Thin Lenses, example
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• Problem 44. Two converging lenses having focal
  lengths of 10.0 cm and 20.0 cm are placed 50.0 cm
  apart, as shown in Figure. The final image is to
  be located between the lenses, at the position
  indicated. (a) How far to the left of the first
  lens should the object be positioned? (b) What is
  the overall magnification? (c) Is the final image
  upright or inverted?

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Problem 61

• The lens makers equation for a lens with
  index n1 immersed in a medium with index n2 takes
  the form
• 1/f(n1/n2-1)(1/R1-1/R2)
• A thin diverging glass lens (index 1.50)
  with R1 3.00 m and R2 6.00 m is surrounded
  by air. An arrow is placed 10.0 m to the left of
  the lens.
• Determine the position of the image.
• Repeat with the arrow and lens immersed in
• water (index 1.33)
• (c) a medium with an index of refraction of 2.00.

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Spherical Aberration

• Results from the focal points of light rays far
  from the principle axis are different from the
  focal points of rays passing near the axis
• For a mirror, parabolic shapes can be used to
  correct for spherical aberration

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Chromatic Aberration

• Different wavelengths of light refracted by by a
  lens focus at different points
• Violet rays are refracted more than red rays
• The focal length for red light is greater than
  the focal length for violet light
• Chromatic aberration can be minimized by the use
  of a combination of converging and diverging
  lenses

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Conceptual questions
Question 4. Explain why a mirror cannot give rise
to chromatic aberration. Question 15. Why does a
focal length of a mirror not depend on the mirror
material when the focal length of a lens depends
on the lens material?
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True or false?
(a) The image of an object placed in front of a
concave mirror is always upright. (b) The height
of the image of an object placed in front of a
concave mirror must be smaller than or equal to
the height of the object. (c) The image of an
object placed in front of a convex mirror is
always upright and smaller than the object.
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Review questions

• 1. What is the focal length of a flat mirror?
• a. 0
• positive
• infinite
• Negative
• 2. The magnification of a 3 cm object placed 5 cm
  from a certain lens is -1. What is the focal
  distance of the lens?
• 0.4 cm
• 0.5 cm
• 2.5 cm
• 5.0 cm

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• 3. Which of the following is responsible for
  mirage?
• a. diffraction
• b. reflection
• c. refraction
• d. dispersion
• 4. An alligator sits 1 m below the surface of
  water of index of refraction n1.4. The
  alligators view of objects above the surface is
  restricted to a circular window at the surface of
  radius
• a. 0.5 m b. 1 m
• c. 2 m d. 2.6 m