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Homework Notes. If you are struggling with the homework, start working on it early enough that you can come to office hours if needed. You can go to the help room even when one of us is not there, at least for the first half of the course.

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homework notes
Homework Notes
  • If you are struggling with the homework, start working on it early enough that you can come to office hours if needed.
  • You can go to the help room even when one of us is not there, at least for the first half of the course.
  • Do not email me Wednesday night with homework questions.
chapter 3 mirrors and lenses1
Chapter 3: Mirrors and Lenses
  • Mirrors
    • Spherical mirrors
    • Ray tracing
  • Convex mirrors
    • Image formation
    • Applications
  • Concave mirrors
    • Image formation
    • Applications
  • Lenses
    • Refraction
    • Converging rays
    • Diverging rays
reflection review
Reflection Review
  • Recall our ray tracing of a flat mirror
  • Recall that there are “special” rays that are sufficient for locating the image
clicker question
Clicker Question
  • Which shows the correct location, orientation, and size for the image?

A)

B)

C)

D)

E)

what is the normal to a curved surface and how is it used to find rays
To find the normal to a curved surface at a point where a ray hits that surface (and will be reflected or refracted)

First draw a tangent line to the curve (or tangent plane to the surface)

The normal is perpendicular to that line or plane and going through the point

Once you have drawn the normal you can draw the reflected or refracted ray

What is the normal to a curved surface and how is it used to find rays?
ray tracing spherical mirrors
Ray Tracing & Spherical Mirrors

paraxial rays

radius of curvature

F

C

  • Radius of Curvature: The radius of the sphere the mirror is “cut from”
  • Center of Curvature (C): The center of the sphere the mirror is cut from
  • Focal Point (F): The point where rays from a distance appear to converge
    • For a spherical mirror, the focal point is halfway between the surface and the center of curvature
  • Paraxial Ray: A ray coming on to the mirror parallel to the axis
convex vs concave
Convex vs. Concave
  • Spherical mirrors are drawn in two dimensions, so you have to imagine the 3D mirror this line represents
  • Both convex and concave mirrors obey the same law of reflection, but they make different kinds of images

Convex

Concave

sources of paraxial rays
Sources of Paraxial Rays
  • The rays coming from a distance source can be considered approximately paraxial when they reach a mirror

Convex mirror

  • The rays from a nearby source, such as a candle or bare light bulb, cannot be considered paraxial
special rays convex mirror
Special Rays: Convex Mirror

axis

F

C

Ray 1 Rule:

All rays incident parallel to the axis are reflected so that they appear to be coming from the focal point, F.

special rays convex mirror1
Special Rays: Convex Mirror

axis

F

C

Ray 2 Rule:

All rays that (when extended) pass through C are reflected back on themselves

special rays convex mirror2
Special Rays: Convex Mirror

axis

F

C

Ray 3 Rule:

All rays that (when extended) pass through F are reflected back parallel to the axis.

locating an image convex mirror
Locating an Image: Convex Mirror

axis

F

C

  • Image properties:
  • virtual (behind the mirror)
  • right-side up
  • closer to the mirror than the object
  • smaller than the object.
compare to flat mirror
Compare to Flat Mirror
  • Image properties:
  • virtual (behind the mirror)
  • upside down
  • the same distance from the mirror as the object
  • the same size as the object
clicker question1
Clicker Question
  • The image formed in a convex mirror is smaller than the object. This would make a convex mirror useful for which application?
  • Makeup or shaving mirror
  • Wide-angle mirror, such as on a car or a blind intersection
  • A mirror in a clothing store dressing room
convex mirrors
Convex Mirrors
  • Because the image is smaller than the object, convex mirrors reflect from wider angles than flat mirrors.
concave mirrors
Concave Mirrors

C

F

axis

Ray 1 Rule:

All rays incident parallel to the axis are reflected so that they pass through the focal point, F.

concave mirrors1
Concave Mirrors

C

F

axis

Ray 2 Rule:

All rays that pass through C are reflected back on themselves

concave mirrors2
Concave Mirrors

C

F

axis

Ray 3 Rule:

All rays that pass through F are reflected back parallel to the axis.

image formation concave mirrors
Image Formation: Concave Mirrors

Object location:

Between the center of curvature and the focal point

C

F

  • Image properties:
  • real (in front of the mirror)
  • upside down
  • farther from the mirror than the object
  • larger than the object.
concave mirrors3
Concave Mirrors

Object location:

Between the surface and the focal point

C

F

  • Image properties:
  • virtual (behind the mirror)
  • right-side up
  • farther from the mirror than the object
  • larger than the object.
concave mirrors4
Concave Mirrors

Object location:

Past the center of curvature

C

F

concave mirrors clicker question
Concave Mirrors: Clicker Question

Object location:

Past the center of curvature

C

F

Is the image

Real and magnified

Real and reduced

Virtual and magnified

Virtual and reduced

clicker question2
Clicker Question
  • The inside of a spoon bowl is a concave surface with a radius of curvature of a couple of inches (depending on the spoon). If you hold it about a foot from your face, what will your face look like?
  • Normal size, upside down
  • Normal size, right side up
  • Smaller, upside down
  • Smaller, right side up
concave mirrors application
Concave Mirrors: Application

Because rays coming in parallel, as from a very distant source, are all reflected to the focal point, a receiver placed there will pick up the waves received over the large area of the dish, instead of just the small area of the receiver itself.

concave mirrors application1
Concave Mirrors: Application
  • What if we put a light source at the focal point of a concave mirror?
  • All the rays emitted by the light go through the focal point, and are therefore reflected parallel to the axis of the mirror.
spherical lenses
Spherical Lenses

What if we don’t want to have to look at a reflection to magnify or reduce an image?

We can use refractive optics instead (lenses)

convex glass surface
Convex Glass Surface

axis

F

C

A concave surface is called “converging” because parallel rays converge towards one another

convex glass surface1
Convex Glass Surface

F

C

axis

The surface is converging for both air to glass rays and glass to air rays

concave glass surface
Concave Glass Surface

C

F

axis

A concave surface is called “diverging” because parallel rays diverge away from one another

concave glass surface1
Concave Glass Surface

F

C

axis

Again, the surface is diverging for both air to glass rays and glass to air rays

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