Properties of Reflective Waves

Curved Mirrors

Image close to a concave mirror appear:

Larger than the objectUpright

Image far from a concave mirror appear:

Smaller than the objectInverted or upside down

Another factor that influence image appearance is:

Curvature R = radius of curvature or/ radius of the spherical mirrorC = center of curvature of the mirror

Another factor that influence image appearance is:

Curvature R = radius of curvature or/ radius of the spherical mirrorC = center of curvature of the mirror

Image location can be found using the mirror equation:

(1/p) + (1/q) = (2/r)

Two kinds of images

Real- images that form in front of the mirrorVirtual- images that form behind the mirror

The FOCAL POINT (F) is half way between the center of curvature and the mirrors surfaceThe distance to the focal point is the focal length (f)

(1/p) + (1/q) = (1/f)

Real images form on the front side of the mirrorVirtual images form on the back side of the mirrorThe mirror is drawn so the front side is on the left

Positive numbers indicate the front side of the mirrorNegative numbers indicate the back side of the mirrorThe principal axis runs through the center of the mirror

Positive numbers are above the principal axisNegative numbers are below the principal axis

The measure of the image compared to the objectM- magnification

M= (h`/h) = -(q/p)m

M is positive means the image is upright

M is negative means the image is inverted

1. Parallel to principal axis – through focal point F

2. Through focal point F – parallel to principal axis

3. Through center of curvature C – back along C

A concave makeup mirror is designed so that a person 25.0 cm in front of it sees an upright image at a distance of 50.0 cm behind the mirror. What is the radius of curvature? What is the magnification? Is it real or virtual?

A concave shaving mirror has a focal length of 33cm. Calculate the image position of a cologne bottle placed in front of the mirror at a distance of 93 cm. Calculate the magnification of the image. Is it real or virtual, upright or inverted? Draw a ray diagram.

A pen is placed 11.0 cm from a concave mirror produces a real image 13.2 cm from the mirror. What is the focal length? What is the magnification of the image? If the pen is placed 27.0 cm from the mirror, what is the new position of the image? What is the magnification? Is it real or virtual?

Where do we see convex mirrors?

Diverging mirrorsImage is always virtual or a negative numberFocal point and center of curvature are always behind the mirror

See page 538Table 14-4

A convex mirror with a radius of curvature of 0.550 cm is placed above the aisles in a store. Determine the image distance and magnification of a customer lying on the floor 3.1 m below the mirror. Is the image real or virtual, upright or inverted?

A spherical glass ornament is 6.00 cm in diameter. If an object is placed 10.5 cm away from the ornament, where will its image form? What is the magnification? Is the image real or virtual, upright or inverted? Draw a ray diagram.

A soda bottle is placed 44cm from a convex mirror. If the mirror’s focal length is 33 cm how far from the mirror’s surfaced does the bottle’s image form? What is the magnification? Is the image real or virtual, upright or inverted? Draw a ray diagram.

When light rays do not intersect at a unified point, the observer will see a blurred imageSPHERICAL ABERRATION

To eliminate spherical aberration:Use mirrors with small diametersUse parabolic mirrors

Segments of a Paraboloid (three dimensional parabola)All rays parallel to the principal axis converge at the focal point

Where do we use Parabolic Mirrors?

Two types of telescopesRefracting – combination of lensesReflecting – uses curved lenses and small mirrors

Parabolic mirror (objective mirror) used to focus light