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SPHERICAL MIRRORS

Objective
The objective of this lab is to observe the reflection of light from a spherical mirror, determine the focal length of the mirror and verify the mirror equation.

Background
The law of reflection states that a ray of light will proceed, after reflection, in a direction such that the angle of incidence equals the angle of reflection. These angles are measured from the normal, the perpendicular drawn to the surface at the point of incidence.

Figure 1, Figure 2

The center of curvature, C, is the center of the spherical surface of which the mirror is a part, it is equal to the radius of the sphere. A concave mirror is formed from the inside surface of the sphere, while a convex mirror is formed from the outside surface of the sphere. The focal point, f, is the point of convergence for an incident beam of parallel light rays. The distance from the focal point to the mirror is called the focal length, it is equal to one half the center of curvature. The principal axis is the line through the center of curvature and the focal point.

The distance from the object to the mirror is called the object distance, s. The distance from the mirror to the image is called the image distance, s'.

The location and size of the image can be graphically determined by finding the intersection point of three principal rays. (Refer to figure 2.)

1. A ray parallel to the axis, after reflection passes through the focal point of a concave mirror or appears to come from the focal point of a convex mirror. (Parallel ray)
2. A ray through (or proceeding toward) the focal point is reflected parallel to the axis.
3. A ray along the radius through the center of curvature intersects the surface along the normal and is reflected back along its original path. (Chief ray or radial ray)

The relationship between the focal length, the object distance and the image distance is given as the mirror equation.

Equipment
- optical bench
- object light box w/ power supply
- spherical mirror
- screen
- Lamp

Procedure
1. Determine the focal length of the mirror. This is accomplished by using an object located at a large distance from the mirror. Remove the mirror from the optical bench and hold a piece of paper, an index card or the screen in front of the mirror in such a way that the image of the far away object is focused on the paper. (You may focus on an object out the window or use one of the ceiling lights in the hallway.) Determine the focal length by measuring the distance from the mirror to the paper.
2. Return the mirror to the optical bench and turn on the object box light source. Place the object about 50 cm from the mirror. Set the screen to a position where a sharp image of the object is observed. Record both the object distance and the image distance. Make note of the size and orientation of the image. Repeat this procedure for six different object distances including the following:
- object beyond the center of curvature, C.
- object at C.
- object between f and C.
3. Now, turn the light box control down to dim the object, set the object inside the focal length of the mirror. In this position the light reflecting from the mirror does not converge to form a real image. Look straight into the mirror to observe the virtual image behind the mirror.

Analysis
By expressing the mirror equation in the form: 1/s = -1/s’ + 1/f the graph of (1/s) versus (1/s’) will be linear with a slope of (-1) and will have an intercept of (1/f).

Determine the values for (1/s) and (1/s’) and graph (1/s) versus (1/s’). Determine the intercept and the slope of the graph. Compare the focal length determined from the intercept value of your graph with the focal length determined using parallel light rays.

Related Activities
1. Compare the image size to the object size at each of the different positions, including the case where you produced a virtual image. Which is larger, the object or the image?
2. Compare the orientation of the image relative to the object for each of the different positions, including the case where you produced a virtual image. Is it inverted or upright?