Ray Tracing and Image Formation for Spherical Mirrors

Guide 26-2. Ray Tracing and Image Formation for Spherical Mirrors

The animations below show principal rays being drawn step-by-step in three situations involving spherical mirrors.

Concave mirror with d_o > f
Concave mirror with d_o < f
Convex mirror

Now, here is an example problem: Determine the position, size and orientation of the image of the object in the concave mirror shown to the right.

Solution: Three principal rays (P, F, and C) have been traced from the tip of the object as per the discussion in the text. Their intersection is the tip of the image. The image is real (light rays actually converge there), inverted, and smaller than the object.

Taking measurements directly from the diagram (grid units of centimeters), we have:

f = 4.0 cm
d_o = 11.0 cm
d_i = 6.3 cm
h_o = 3.0 cm
h_i = -1.7 cm

Note the positive signs on object and image distances, indicating that they're both on the reflecting side of the mirror. Note also the negative sign on the image size, indicating that it's inverted.

Let's check to see if the measured distances agree with known quantitative relationships.

We should have d_o/d_i = -h_o/h_i. We'll calculate each ratio separately and then compare.

d_o/d_i = 11.0/6.3 = 1.7
-h_o/h_i = -3.0/(-1.7) = 1.8

The results agree to 2 significant figures.

Now let's check the mirror equation: 1/d_o + 1/d_i = 1/f. Again, we'll calculate each side separately and compare.

1/d_o + 1/d_i = (1/11.0 + 1/6.3) 1/cm = 0.25 1/cm
1/f = 1/4.0 1/cm = 0.25 1/cm

Again, the results agree.