Curved mirrors

General info

Drawing ray diagrams

LOCATION OF CURVED MIRRORS IN THE WORLD

Other objects that act like a curved mirror

Example where the concentration of light to one location (focal point)

is used to heat water

Solar oven

Focal point

• Place where all parallel light rays meet after they reflect off a concave mirror

• Distance from mirror to closest point on mirror is focal length

The reverse is also true

• If light passes through or originates from the focal point, then the reflected rays will be parallel to the PA

Examples of use

OTHER PARTS OF THE ELECTROMAGNETIC SPECTRUM ACT THE SAME WAY AS LIGHT

Dishes

TYPES OF CURVED MIRRORS

Convex and Concave

• Convex • Concave

CONCAVE MIRRORS

5 concave

• Locations for the object

– Beyond CP– At CP– Between CP and FP– At FP– Between FP and V

When object is between V and F

• Rays will diverge

• To find virtual image, extend the reflected rays across the mirror to the opposite side

These extensions are called the apparent light rays and are used by the mind to form virtual image

CONVEX MIRRORS

Draw 2 more diagrams

• 1 where the object is far away from the mirror

• 1 where the object is close to the mirror

Convex mirror ray diagrams

• Different side of the curve is mirrored

RAY DIAGRAMS FOR CURVED MIRRORS

Graphical interpretation of the reflection of light off curved mirrors

BASIC FEATURES ON ALL DIAGRAMS

Determine location of images

• Two methods

Graphical

Mathematical

Graphical Method to determine image characteristics

• This method will be able to determine images:

LocationRelative size (compared to object)Orientation (relative to Principal axis)if image is Virtual or Real

General preparations

• Find something that can be used to make the curve of the mirror

• Fold paper hot-dog style

• Draw line down fold, label principal axis

Principal axis

• Line that splits mirror in half

• Goes through vertex point

• Label vertex point V

Drawing the mirror

• We will work with a cross-section image of the mirror

• Show the paths of light rays that reflect off mirror

• Curved section of protractor becomes cross section of mirror

Draw a concave mirror on your paper

• Place protractor on right end of paper

• Center protractor on Principal axis (PA)

• Make sure mirror is concave towards rest of the paper

Location of vertex

• Intersection of principal axis and mirror

Center Point of curvature

• DO NOT remove protractor from paper

• Mark the center point of the protractor on the PA. Label “C”

• This is the center point

Focal point

• Point in front of the mirror, where all rays parallel to principal axis will reflect through

Location of focal point

• Focal point is located halfway between the center point and the vertex

Draw an object

• Need to draw a cross section of an object

• Bottom rests on PA– Try a banana, rectangle or arrow– Draw about ¾ of an inch high– Location of object relative to mirror will be

different for each diagram

For each drawing:

1. Title in upper left corner of drawing

2. PA, C, F, V all drawn or labeled

3. 2 light rays must be drawn

4. Image drawn in correct place, orientation

Hints for good drawings:

• Use a thin object ¾ to 1 inch tall

• Need one more type of ray path that does not involve the focal point

• Most mirrors drawn to the far right of paper– Except for the object place between F and V– Put mirror in middle of paper

PATHS TAKEN BY LIGHT ON DIAGRAMS

General idea

• Light can bounce off an object and travel in all possible directions

• To find the position of the image, find the location where at least 2 light rays intersect that reach your eyes

The 4 easiest rays to draw

• Of all the countless possible rays to use, 4 paths are used because they pass through specific points, move parallel to the principal axis and/or where angle of incidence = angle of reflectance

Common light paths traveled

How rays reflect off concave mirror

Remember

• Virtual images are formed in your mind, where apparent light rays meet.

• Real images are formed when real light rays that bounce off the mirror intersect in space.

How to draw the rays for convex mirror

Converging rays, diverging rays

• Converging rays come together at a point

• Diverging rays do not intersect

RESULTS WHEN SOURCE OF LIGHT IS INFINITELY FAR AWAY

Where is image formed from sunlight, moonlight or the light of

stars?• The distance from those objects to earth can

be considered infinitely far away.

• The only rays of the sun that intersect one point of the earth are all parallel to each other

• The image will form on a plane perpendicular to the principal axis that includes the focal point

Spherical Aberration

• Inaccuracies introduced into the diagrams because the curve used was part of a circle instead of a parabola

• All intersections of light paths will not form on the image plane

• We use a circle because it is easier to create with the material at hand