Lenses

Introduction

The purpose of this laboratory exercise is to investigate image formation by lenses. An optical bench 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). Notice how the converging lens brings the rays together, so the blue and green form another color, nice aqua (Figure 2a), while diverging lens separates rays (Figure 2a).

Figure 1. Converging lens

Figure 1a. Converging lens brings rays together

Figure 2. Diverging lens

Figure 2a. Diverging lens separates rays

The converging lens is used as a magnifying glass, while the diverging lens makes objects look smaller and farther away (Figure 3a, b, c, and d).

Figure 3a. Magnifying effect of a converging lens

Figure 3b. Reducing effect of a diverging lens

Figure 3c. Magnifying effect of a converging lens

Figure 3d. Reducing effect of a diverging lens

Ray Diagrams

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 diagrams below show three:

The parallel ray (red) is the ray that originates at the very top of the object and travels toward the lens parallel to the axis of symmetry. That ray will pass through the focal point of the lens (Figure 4)
The focus point ray (green) is 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)
The central ray (blue) is 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)

Figure 4. Parallel ray

Figure 5. Focus point ray

Figure 6. Central ray

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

1. Lens Diagram

In the first part of the lab, we will find the image using the ray diagram technique (see above). Your task is to determine the image's distance from the lens and its properties using parallel and central rays.

The worksheets will be provided in class.

2. Optical Bench

In this part of the lab, we will use the optical bench (Figure 7). Place the object, the screen, and the lens on the optical bench as shown in Figure 8. You may want to place the screen in a way that the sunlight does not interfere with the image created on the screen (Figure 9).

Figure 7. Adjusting the lens' position.

Figure 8. Source-lens-screen set.

Figure 9. Image on the screen.

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 10). Write a brief summary of your findings.

Figure 10. Data collection table.

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

Replace the lens with a diverging one. Write a brief summary of your findings.

Part C. Relationship between the distance of the image and the distance of the object.

Select a converging lens.

Place the screen at the far end of the optical bench. Move the lens until you see a sharp image on the screen. Take the distance of the object d_o and the distance of the image d_i.

Move the screen a little bit closer to the lens and adjust the lens so you could see a sharp image. 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 (d_o goes on the horizontal axis, d_i goes on the vertical one).

Plot the points.
Plot the best fit line using the equation 1/x + 1/y = 1/a. Manually adjust the "a" coefficient so the curve passes through your experimental points. Interpret the "a" coefficient.
You can use the Lens' Equation in Desmos as a hint.

Part D. Relationship between the distance of the image and the distance of the object.

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

You can compare your results with those published on the Physics Lab Blog.

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