6.6 - Image Formation by Spherical Mirrors

Types of Mirrors and Fields of Vision

• A spherical mirror is part of a hollow sphere. A concave mirror reflects from the inner surface; a convex mirror reflects from the outer surface.
• The inner and outer surfaces of a shiny steel spoon act as concave and convex mirrors respectively.
• For mirrors of the same size, a convex mirror gives a wide field of vision, a plane mirror a narrower field and a concave mirror a very narrow field.

Optical Terms

Term	Meaning
Principal axis	Straight line through centre of curvature $C$ and mirror pole $P$.
Centre of curvature, $C$	Centre of the sphere from which the mirror is formed.
Radius of curvature, $r$	Distance from $P$ to $C$.
Focal point, $F$	Point on the principal axis where reflected parallel rays converge for a concave mirror, or appear to diverge from for a convex mirror.
Object distance, $u$	Distance from object to $P$.
Image distance, $v$	Distance from image to $P$.
Focal length, $f$	Distance from $F$ to $P$.

• Radius of curvature is twice the focal length:

Principal Rays for Spherical Mirrors

Concave mirror	Convex mirror
A ray passing through $C$ reflects back along its original path.	A ray directed towards $C$ reflects back along its original path.
A ray parallel to the principal axis reflects through $F$.	A ray parallel to the principal axis reflects as if from $F$ behind the mirror.
A ray passing through $F$ reflects parallel to the principal axis.	A ray directed towards $F$ reflects parallel to the principal axis.

• Intersect reflected rays to locate a real image; extend them backwards to locate a virtual image.

Image Position and Characteristics

Object position for a concave mirror	Image position and characteristics
At infinity	At $F$, $v=f$, in front of the mirror; real, inverted, diminished.
Beyond $C$: $u>2f$	Between $F$ and $C$, $f<v<2f$, in front; real, inverted, diminished.
At $C$: $u=2f$	At $C$, $v=2f$, in front; real, inverted, same size.
Between $F$ and $C$: $f<u<2f$	Beyond $C$, $v>2f$, in front; real, inverted, magnified.
At $F$: $u=f$	Reflected rays are parallel; image at infinity.
Between $F$ and $P$: $u<f$	Behind the mirror, image distance greater than object distance; virtual, upright, magnified.

• For a convex mirror, the illustrated objects beyond $F$ or between $F$ and $P$ form a virtual, upright, diminished image behind the mirror between $P$ and $F$, with image distance less than the focal length.

Applications of Concave and Convex Mirrors

Application	Reason for using the mirror
Concave cosmetic mirror	Magnifies the face to assist make-up.
Concave dental mirror	Gives an upright, magnified image for examining teeth.
Concave parabolic car-headlight reflector	Maintains light intensity at a distance, especially during night driving.
Convex blind spot mirror	Widens a driver’s view at dangerous sharp corners.
Convex security mirror	Allows surveillance in buildings and shopping centres.
Convex vehicle rear-view mirror	Gives a wide field of vision to see vehicles approaching from behind.