Curved Mirrors

• The most common type of curved mirror is a spherical mirror

• A spherical mirror has the shape of a section from the surface of a sphere

Curved Mirrors

• Concave mirror – the inside surface of the mirror is polished• Convex mirror – the outside surface

of the mirror is polished

Curved Mirrors• Law of Reflection still applies! • angle of incidence = angle of reflection• The normal line is drawn perpendicular

to the mirror at the point of incidence.

Concave Mirrors

• C is the center of curvature• R is the radius of curvature (distance

between C and the mirror)• Principal axis – a straight line drawn

through C and the midpoint of the mirror

Concave Mirrors

• If the object is infinitely far from the mirror, the rays are parallel to each other and the principal axis• These rays reflect from the mirror and

pass through the focal point, F • f- focal length is the distance from F to

the mirror

Concave Mirrors

• F is halfway between C and the middle of the mirror• f=1/2R

Convex Mirrors

• F is halfway between C and the middle of the mirror• f=-1/2R• by convention, we use a negative sign

for the focal length of a convex mirror

The formation of images by mirrors

• Light rays emanate from an object, strike the mirror, reflect from it, and form an image.• Ray Tracing is a graphical method of

analyzing the image produced by either concave or convex mirrors.

CONCAVE MIRRORS

• RAY1: The ray emanates from the object parallel to the principal axis. It strikes the mirror and reflects through the focal point.

CONCAVE MIRRORS

• RAY2: The ray emanates from the object and passes through the focal point. It strikes the mirror and reflects back parallel to the principal axis.

CONCAVE MIRRORS

• RAY3: The ray travels along a line that passes through the center of curvature, C, strikes the mirror and reflects back on itself.

CONCAVE MIRRORS

• If Rays 1,2 and 3 are superimposed on a scale drawing, they converge at a point that defines the top of the image.

CONVEX MIRRORS• RAY1: The ray emanates from the object

parallel to the principal axis. It strikes the mirror and reflects but appears to originate from the focal point F

CONVEX MIRRORS• RAY2: The ray emanates from the object

and heads towards F, reflecting parallel to the principal axis after reflection.

CONVEX MIRRORS• RAY3: The ray emanates from the object

and heads towards C, reflecting back on itself.

CONVEX MIRRORS• The 3 rays appear to come from a point

on a virtual image behind the convex mirror.