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Lenses SMU Physics 142L – 172L

Purpose: This lab will explore the optical properties of convergent lenses. You will find the focal length of several lenses by three methods. Once the focal lengths are known, you will determine the refractive index of the glass used to make the lenses.

Introduction: Lenses can be either convergent (+) or divergent (-). Convergent lenses focus (converge) parallel light rays entering the lens at a focal point. The distance from the center of the lens to that focal point is the focal length of the lens. The focal length is dependent on the refractive index of the lens material and radius of curvature of the lens surfaces. Divergent lenses will take the same parallel light rays and bend them away from each other:

Convergent lens

Divergent lens

Focal Point

In this lab we will be using symmetric converging lenses with focal lengths between 5 and 25 cm, although if you are looking for a challenge, there are asymmetric lenses available—just ask.

Procedure: Choose at least two lenses to work with. Each lens must have a focal length at least two cm different than the other lens(es) you will be using. No more than one lens can have a diameter of less than 6cm. The following methods for determining focal length can be performed in any order, although the diopter method will give the quickest determination that the focal lengths are sufficiently different.

Far Object Method: Assemble the optical bench with a lens holder (with lens) and a screen as shown. Ensure center of lens and screen are at the same height.

Lens

Screen

Outside, point the optical bench at some distant object with sharp angles and/or high contrast (the chapel works well.) Adjust the screen to bring the projected image into the best focus. The thin lens equation to determine focal length is: where f is the focal length, do is the distance from the lens to the object, and di is the distance from the lens to the image. Because the distance to the object is very large relative to the distance to the image, the light rays from the object can be considered to be parallel, and the distance from the lens to the image is the same as the focal length. (The limit of as do approaches ∞ is 0)

Near Object Method: Assemble the optical bench with a light source, object, lens holder (with lens) and screen as shown. Ensure center of light, object, lens and screen are at the same height.

Lens

Screen

Object

Lamp

Adjust the object and the screen to bring the projected image into the best focus. The same thin lens equation applies, but the distance from lens to object must be included: . Note the orientation and size of the image. Use at least two different object distances to find an average focal length for each lens.

The magnification can be found by the equation where hi is the height of the image and ho is the height of the object. This can be compared to the theoretical magnification where do is the distance from the lens to the object, and di is the distance from the lens to the image.

Diopter Method: Place the lens in the diopter meter and adjust the dial to bring the light pattern into the best focus. The diopter reading is then taken directly from the dial. The diopter value is in m-1. The focal length can be found by taking the reciprocal of the diopter reading.

Spherometer: Once the focal length is determined for each lens, the refractive index can be determined with the lensmaker’s formula:

f is the focal length, n is the refractive index, r1 and r2 are the radii of curvature of each side of the lens. The negative sign reflects that the radii of the curves on each surface of the lens are in the opposite direction. Since all of the lenses we will be using are convex on both sides, you can consider the equation to be If you are using a symmetric lens, the formula becomes: To determine the refractive index (n) you will now need to determine the radius of curvature using the spherometer. The spherometer can be thought of as a special purpose micrometer designed for measuring the curve of a spherical surface. The principle digit is read from the post at the top of the wheel, and the decimal places can be read from the top of the wheel at the front of the post. The spherometer is placed on the lens as shown at the top of the following page: (You are looking at the top of the lens from the side)

Distance from center point to edge point of spherometer (d)

Height of curve (h)

Radius of curvature (R)

Analysis: Determine the focal length of each of your lenses by the three methods described. Use the average of those three focal lengths, the radius you determine using the spherometer and the lens maker’s formula to determine the refractive index of the lens material. Compare that to the value given in your text for lens glass. Compare the observed magnification in the “near object method” to the theoretical magnification.

Lab Evaluation – Please provide feedback on the following areas, comparing this lab to your previous labs: How much fun you had completing this lab; How well the lap prep period explained this lab; The amount of work required compared to the time allotted; Your understanding of this lab; The difficulty of this lab; How well this lab tied in with the lecture. Please assign each of the listed categories with a value from 1-5, with 5 being the best, 1 the worst. Comments supporting or elaborating on your assessment can also be very helpful in improving the future labs.

Date Last Modified Mar 26, 2010 Page Number 4

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