Calculate distances and focal lengths using the mirror equation for concave and convex spherical mirrors.

Draw ray diagrams to find the image distance and magnification for concave and convex spherical mirrors.

Distinguish between real and virtual images.

Differentiate between parabolic mirrors andspherical mirrors.

Concave Mirrors A concave spherical mirror is a mirror

whose reflecting surface is a segment of the inside of a sphere.Reflects light from its inner “caved in”

surface Concave mirrors can be used to form real

images.

Real vs. Virtual Images A real image is an image formed when

rays of light actually converge and pass through a point on the image. Real images can be projected onto a

screen. Virtual images are behind a plane

mirrorThe rays reflected never actually converge

but appear to diverge from behind the mirror

The radius of curvature, R, is one factor that determines the size and where the image will appear

R is the distance from the mirror’s surface to the center of curvature, C

C is the geometric center of the sphere Principle axis is the straight line

perpendicular to the center of the surface of the mirror

F is the focal point: where the reflected rays cross the principal axis; parallel rays converge at F

f is the focal length of the mirror which is the distance from F to the mirror along the principal axis

2f=R

Locating images in mirrors by ray tracing1. Determine scale of drawing

a. If object is beyond F, then image will be on object side of mirror. Draw mirror on right side of paper

b. If the object is beyond C, the image distance will be small, so draw object near left side of paper

c. If object is between C and F, the image will be beyond C. The closer the object is to F, the farther away the image will be, so image will be near left side of paper

2. Draw the principal axis. a. Draw vertical line where principal axis

touches mirror.b. If the focal point is known, indicate

that position on the principal axis and label it F.

c. Identify and label center of curvature, C (it is twice the focal distance, f, from mirror)

3. Draw object

4. Draw ray 1 from top of object parallel to principal axis. (All rays parallel to principal axis are reflected through F)

5. Draw ray 2 from top of object through F. (It will be reflected parallel to principal axis)

6. Draw ray 3 from top of object through C.7. The image is located where any two rays

intersect. The third ray is used to check. Draw line to principal axis to represent image

Practice ProblemThe focal length is 20.0 cm. Draw a ray diagram to identify where each image is formed.

1. Object is at C2. Object is at F3. Object is between C and F 4. Object outside C5. Object inside F

You can use the mirror equation below to predict the image location.

p and q have a positive value if they are on the front side or reflecting side of the mirror.Real images

q has a negative value if the image is on the back side of the mirror.Virtual image

f is positive for concave mirrors.

h is positive if it is upright and negative when inverted.

M is positive for virtual (upright) images and negative for inverted images.

Geometry shows that the ratio between image and object height is the same as the ratio between image and object distance.

The negative sign is required because images on the back side of the mirror have negative image distances.

Practice problemA concave spherical mirror has a focal length of 10.0 cm. Locate the image of a pencil that is placed upright 30.0 cm from the mirror. Find the magnification of the image. Draw a ray diagram reference.

Spherical aberration With spherical mirrors, rays not near

the principal axis do not all meet at the image point (spherical aberration, which causes blurry images)

Parabolic mirrors eliminate this problem and produce sharper images

(reflecting telescopes). Paraxial rays are very near the

principal axis, make the assumption that all the rays in drawings and calculations are paraxial even if they may not appear to be.

Convex Mirrors Spherical mirror whose reflecting surface

is outward-curved segment of a sphere Also called diverging mirror

○ Reflected rays spread outSide-view mirrors on cars

Image is always virtual and smaller than objectAppears to be farther away

○ “Objects may be closer than they actually appear”

Convex Ray Diagrams F is behind the mirror

Still half way between C and mirror If using mirror equations, f is negative,

image distance is also negative

Convex Ray Diagrams Ray 1: from top of object parallel to

principal axisReflected ray: draw dashed line from F to

point where ray 1 strikes mirror, continue line past mirror

Ray 2: approaches mirror on a path that, if extended behind mirror, would pass through FReflected ray: parallel to principal axis,

continue it behind mirror.