Spherical Mirrors

Introduction

The purpose of this laboratory exercise is to investigate the image formation by mirrors. The animation below will be used to analyze properties of the image and to collect information about the image distance as a function of the object distance.

Theory

There are three sorts of mirrors: plane mirror (Figure 1), converging (concave) mirror (Figure 2), and diverging (convex) mirror (Figure 3).

Any object is a source of light (either emitted or reflected) that can be modeled with numerous rays. These rays are represented by lines, which is why that branch of physics is called geometric optics.

In order to find an image created by a spherical mirror, just two characteristic rays are needed. The simulation below shows three:

1. The parallel ray (red) - the ray that originates in the very top of the object travels toward the mirror parallel to the axis of symmetry and is reflected back through the focal point (Figure 4)

2. The focus point ray (green) - the ray that originates in the very top of the object travels toward the mirror through the focal point and is reflected back parallel to the axis of symmetry (Figure 5)

3. The central ray (blue) - the ray that originates in the very top of the object travels toward the center of the mirror and is reflected back symmetrically (Figure 6)

These rays intersect in one point and form the image. Notice the symmetry of the red and green ray; the parallel incidence ray is reflected back through the focal point, the one that passes through the focal point is reflected back parallel.

Experimental Procedure

The application below allows moving the object away from or closer to the mirror. The image is automatically created. Both center of the mirror curvature and the focus point are clearly indicated (Figure 7). Set of sliders can be used to move the object. The desired mirror can be selected at the bottom of the experimenter dashboard (Figure 8).

Part A. Properties of the image created by converging mirror.

There are three properties of an image formed by a mirror: location, orientation, and size. If the image is located at the same side of the mirror as the object, it is real; otherwise, it is virtual. If the image is in the same direction that the object, it is upright; otherwise, it is inverted. If the image is smaller in size than the object, it is reduced; otherwise, it is magnified.

Place the object in assigned position (follow the first column in the table below) and find out whether the image is real or virtual, upright or inverted, magnified or reduced. Collect your findings in a table (Figure 9). Write a brief summary of your findings.

Simulation

Part B. Properties of the image created by diverging mirror.

Select the diverging mirror on the experimenter dashboard (Figure 8). Collect your findings in a table (Figure 9). Write a brief summary of your findings.

Part C. Relationship between distance of the image and distance of the object (short focal length).

Select a converging mirror. Choose magnitude of the focal length such as 30 cm < f < 50 cm.

Place the object far away form the mirror. Take the distance of the object d_o and the distance of the image d_i. Move the object a few centimeter closer to the mirror. Take the distances. Repeat several times. Based on the data collected that way, create a graph of d_i as a function of d_o. Paste the graph to your Lab Report. Interpret the graph.

Plot 1/d_o + 1/d_i = 1/f [or, using mathematical notation, 1/x + 1/y = 1/a]

Does the curve pass through your experimental points?

Part D. Relationship between distance of the image and distance of the object (long focal length).

Choose magnitude of the focal length such as 50 cm < f < 100 cm.

Repeat the data collection and graphing procedure.

Source of the simulation: http://physics.bu.edu/~duffy/HTML5/Mirrors.html