The equation 1/p + 1/i =2/r for spherical mirrors is an approximation that is valid if the image is formed by rays that make only small angles with the central axis. In reality, many of the angles are large, which smears the image a little. You   can determine how much. Refer to Fig. 34-22 and consider a ray that leaves a point source (the object) on the central axis and that makes an angle α with that axis.

First, find the point of intersection of the ray with the mirror. If the coordinates of this intersection point are x and y and the origin is placed at the center of curvature, then y = (x + pr) tan α and x2 + y2 = r2, where p is the object distance and r is the mirror”s radius of curvature. Next, use tan β = y/x to find the angle γ at the point of intersection, and then use α + γ = 2β to find the value of γ. Finally, use the relation tan γ – y/(x + ir) to find the distance i of the image.

(a) Suppose r = 12 cm and p = 20 cm. For each of the following values of α, find the position of the image-that is, the position of the point where the reflected ray crosses the central axis: 0.500, 0.100, 0.0100 rad. Compare the results with those obtained with the equation 1/p + 1/i = 2/r. (b) Repeat the calculations for p = 4.00 cm.


Fig. 34-22 A concave spherical mirror forms arcalpoint image Iby reflecting light rays from a point.

Do You Need A Similar Assignment?

Place an order with us. Our skilled and experienced writers will deliver a custom paper which is not plagiarized within the deadline which you will specify.

Note; 6 Hours urgent orders deliver also available.

If you need more clarifications contact our support staff via the live chat for immediate response.


Type of paper Academic level Subject area
Number of pages Paper urgency Cost per page: