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 Lenses

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• Recall our ray tracing of a flat mirror• Recall that there are “special” rays that are

sufficient for locating the image

Clicker Question• Which shows the correct location, orientation,

and size for the image?

A)

D) E)

C)B)

Spherical Mirrors

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

Ray Tracing & Spherical Mirrors

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

CF

radius of curvature

paraxial rays

Convex vs. Concave

Convex 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

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

CFaxis

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 Mirror

CFaxis

Ray 2 Rule: All rays that (when extended) pass through C are reflected back on themselves

Special Rays: Convex Mirror

CFaxis

Ray 3 Rule: All rays that (when extended) pass through F are reflected back parallel to the axis.

Locating an Image: Convex Mirror

CFaxis

Image properties:•virtual (behind the mirror)•right-side up•closer to the mirror than the object•smaller than the object.

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 Question

• The image formed in a convex mirror is smaller than the object. This would make a convex mirror useful for which application?

A. Makeup or shaving mirrorB. Wide-angle mirror, such as on a car or a blind

intersectionC. A mirror in a clothing store dressing room

Convex Mirrors• Because the image is smaller than the object,

convex mirrors reflect from wider angles than flat mirrors.

Concave Mirrors

C Faxis

Ray 1 Rule: All rays incident parallel to the axis are reflected so that they pass through the focal point, F.

C Faxis

Concave Mirrors

Ray 2 Rule: All rays that pass through C are reflected back on themselves

Concave Mirrors

C Faxis

Ray 3 Rule: All rays that pass through F are reflected back parallel to the axis.

Image Formation: Concave Mirrors

C F

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

Object location: Between the center of curvature and the focal point

Concave Mirrors

C F

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

Object location: Between the surface and the focal point

Concave Mirrors

C F

Object location: Past the center of curvature

Concave Mirrors: Clicker Question

C F

Object location: Past the center of curvature

Is the image

A.Real and magnifiedB.Real and reducedC.Virtual and magnifiedD.Virtual and reduced

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?

A. Normal size, upside downB. Normal size, right side upC. Smaller, upside downD.Smaller, right side up

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: 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

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

CFaxis

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

Convex Glass Surface

C Faxis

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

C Faxis

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

Concave Glass Surface

CF axis

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

Concave Glass Surface