Physics II: REFLECTION BY A SPHERICAL MIRROR
LAM 3/12/99
Objective: To measure the focal length of a concave mirror and to demonstrate the mirror equation.
Apparatus: Optical bench, object-grid screen, white screen, screen holder, concave mirror, mirror holder,
and light source.
Theory: By applying the laws of reflection to a spherical mirror, one may derive the mirror equation:
1 1 2
+ =
(1)
s s′ R
Where s is the distance measured from the mirror to the object (Fig. 1). With incident light from the left to
right, s, the object distance, is positive if the object lies at the left of the mirror, R, the radius of curvature
of the mirror surface, is positive if the mirror is concave or negative if it is convex and s′, the image
distance, is positive if the image is real and is on the left of the mirror. If s′ is negative the image is said to
be virtual. In such a case the rays appear to diverge from a point behind the mirror, but no image can be
found on the screen.
By definition, the focal length of a mirror is the distance from the mirror to the point at which light will
focus when coming from an infinite distance. Hence, in the above equation, when s = ∞, s′ ≡ f, so f = R/2.
We may thus write the mirror equation as
1 1 1
+ =
s s′ f
(2)
The reflection of a ray by a concave spherical mirror is shown in Fig. 1.
Figure 1. Positive directions for the mirror equation variables.
The focal length of a concave mirror may be determined either from the definition of the focal length or
through use of the mirror equation. Convex mirrors require more complicated procedures.
Procedures:
1. The focal length may be found by using the definition. Take the optical bench (assembled as shown
in Figure 2) to a window and vary the white image screen distance to form a sharp image. Since the
distant object is far away, the image distance, s' ≅ f. [Note how the optical bench is held at a slight
angle so the incoming rays clear the white image screen. If necessary, tilt the mirror in its holder to
form the image on the white image screen.]
Figure 2. Utilization of a distant object for focal length determination.
2. The mirror equation may be used quickly and effectively to determine the focal length of the
concave mirror. With the optical bench assembled according to Figure 3, adjust the mirror position
until a sharp image of the object grid (a metal grid) appears below the object. Substitution of the
measured value of s (also = s') in the mirror equation yields the focal length of the mirror. This
procedure is called the "coincidence method".
Figure 3. Determination of the focal length with equal object and image distances.
3. The mirror equation may also be used to determine the focal length when the object and the image
distances are unequal. With the optical bench assembled as shown in Figure 4 [object near one end
& mirror at other end], move the white image screen until a sharp image appears. Use the measured
values of s and s' in the mirror equation to determine the focal length of the concave mirror.
Figure 4. Determination of the focal length with unequal object and image distances.
4. In a titled table list your s, s', and f values for procedures 1 - 3. Compute an average f.
4. From your average f value compute a value for the radius of curvature of the mirror.
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In addition to the table and other results, your report should include a concluding paragraph concerning
sources of error and other comments on this report.