Lenses

Introduction

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

Theory

There are two sorts of lenses: converging lens (Figure 1), and diverging lens (Figure 2). Optical instruments are various combinations of the converging and diverging lenses (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 lens, just two rays are needed. The simulation below shows three:

1. The parallel ray (red) - the ray that originates at the very top of the object travels toward the lens parallel to the axis of symmetry. That a\ray will pass through the focal point of the lens (Figure 4)

2. The focus point ray (green) - the ray that originates at the very top of the object and travels toward the lens through the focal point. That ray is parallel to the axis of symmetry after passing through the lens (Figure 5)

3. The central ray (blue) - the ray that originates at the very top of the object and travels toward the center of the lens. That ray does not change its path (Figure 6)

These rays intersect at one point and form the image. Notice the symmetry of the red and green ray; the parallel incidence ray passes through the focal point, the one that passes through the focal point is parallel on the other side of the lens.

Experimental Procedure

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

Part A. Properties of the image created by a converging lens.

There are three properties of an image formed by a lens: location, orientation, and size. If the image is located behind the lens, it is real (the real rays form the image); otherwise, it is virtual (the image is created in our brain based on the assumption that the diverging rays were scattered on an existing object. 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 the assigned position 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 the diverging lens.

Select the diverging lens 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 the distance of the image and the distance of the object (short focal length).

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

Place the object far away from the lens. Take the distance of the object d_o and the distance of the image d_i. Move the object a little bit closer to the lens. 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 the distance of the image and the distance of the object (longer focal length).

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

Repeat the data collection and graphing procedure described in Part C.

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