Major Concepts in Physics Lecture 11.

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Major Concepts in Physics Lecture 11.

• Prof Simon Catterall
• Office 309 Physics, x 5978
• smc_at_physics.syr.edu
• http//physics/courses/PHY102.08Spring

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Anouncements

• Exam 2 Wednesday March 5 in class
• Online exam sample plus solutions, homework2
  solutions, quiz 2 solutions
• Material everything from lecture 8-12 inclusive
  (thermal radiation, line spectra, color mixing,
  ray approx, mirrors, lenses, polarization)
• Similar in format/style/grading to exam 1
• Review session in class on Monday March 3

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Plan for today

• Recap basic features of geometrical optics ray
  approx, reflection, refraction
• Simple examples of refraction
• Formation of images diverging/converging
  mirrors/lenses. Inversion, magnification, real or
  virtual images
• Simple examples and demos

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Wavefronts, rays

• If wavelength of wave much smaller than size of
  system can use a ray approximation to calculate
  what happens to wave.
• Rays show direction of propagation. At 900 to
  wavefront (locus of wave crests)
• This approx neglects diffraction/interference
  effects
• Often valid for light (l500 nm)

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Reflection and refraction

• When light/wave passes from one medium to another
  eg air?glass one finds
• Reflected ray
• Transmitted ray
• Directions of these rays governed by simple laws
• Reflection angle of incidenceangle of
  reflection
• Snells law n1sin(q1)n2sin(q1)

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The angle of incidence equals the angle of
reflection. The incident ray, reflected ray, and
normal all lie in the same plane. The incident
ray and reflected ray are on opposite sides of
the normal.
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Snells Law
where the subscripts refer to the two different
media. The angles are measured from the normal.
When going from high n to low n, the ray will
bend away from the normal.
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Total Internal Reflection
For angles of incidence greater than the critical
angle there is NO transmitted ray. Need n2ltn1
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Refraction example apparent depth

• A kingfisher spies a fish which appears to be 1.0
  m below the water surface. What is the true depth
  of the fish. Assume the refractive index of water
  is 4/3

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Solution

• Kingfisher sees not only vertical rays but
  rays at a non-zero angle. These are bent at
  water-air interface. Image formed by following
  bent rays backward.
• Use simple trig to relate true and refracted
  angles to real and apparent depth. Use Snell to
  relate in turn to refractive index.
  dapp/dreal1/n3/4

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Spherical mirrors

• Two types diverging and converging named
  according to whether rays diverge/converge after
  reflection
• Possess a focal point a point in space through
  which all rays, which were initially parallel to
  the symmetry axis of the mirror, pass after
  reflection
• Focal point is at distance radius of curvature
  / 2

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Diverging (convex) mirror
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Points to note

• For diverging mirror focal point is behind the
  mirror
• Corresponds to tracing the diverging rays back.
  Image is said to be virtual
• Upright image
• Locate image by drawing at least 2 rays
  typically one that goes through focal point and
  one that passes through center of curvature

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Drawn in green, red, and blue are the principal
rays.

• A ray parallel to the principal axis is reflected
  as if it came from the focal point. (green)
• A ray along a radius is reflected back upon
  itself. (red)
• A ray directed toward the focal point is
  reflected parallel to the principal axis. (blue)

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Converging (concave) mirror

• Image may be real or virtual. Real images
  correspond to points where physical rays cross.
  Can be projected on screen.
• May be upright or inverted.

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Real image
Drawn in green, red, and blue are the principal
rays.

• A ray parallel to the principal axis is reflected
  through the focal point. (green)
• A ray along a radius is reflected back upon
  itself. (red)
• A ray along the direction from the focal point to
  the mirror is reflected parallel to the principal
  axis. (blue)

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Converging mirror virtual image
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Demos

• Diverging/converging mirrors
• Focal points focusing infrared radiation and
  lighting matches .
• Spoons

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Lenses

• Rays are bent not by reflection but by refraction
• Thin lens approx assume angle of bending
  proportional to distance of ray from center of
  lens

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Diverging and converging lenses

• Again all possess a focal point through which
  rays, initially parallel to principal axis, pass
  after transmission through lens
• Also, any ray through center passes through
  without deviation
• Allows us to draw ray diagrams as for mirrors
• Images may be real, virtual, upright or inverted

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Demos

• Simple lens behavior

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Lens/Mirror equation

• Can predict quantitatively the distances of
  images for both lens/mirrors using
• 1/p1/q1/f
• p distance of object from mirror/lens
• q distance of image from mirror/lens q
  negative implies virtual image
• f focal length positive for converging
  mirrors/lens. Negative for diverging.

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Magnification

• Use mirror/lens equation to find say q given p
  and f
• Then use formula for magnification
• mheight object/height image
• m-q/p
• Negative m means inverted image