Physics 425LW Optics Laboratory Thin Lens Geometric Optics

Introduction In this lab you will study thin lenses. You will learn a variety of ways to determine the focal length of lenses and the index of refraction of the material a lens is made from. 1 Theory The theory for these experiments can be found in the chapter on geometrical optics in Pedrotti, Pedrotti, and Pedrotti Introduction to Optics or another similar book. 2 The Experiment 2.1 Apparatus You will have the following items to perform these experiments. See the appendix for photographs. • meter stick • lenses • optical rail setup (including carriages, posts, post holders, etc.) • light source • objects mounted on glass microscope slides in mount • recessed screen, frosted glass screen • 500 µm pinhole • adjustable flat front surface mirror • 0.025 inch wire grid in holder • spherometer 2.2 Setup Optical Alignment • Alignment is quite important in most optical experiments. Before we start with the experiments we will align the components on the optical bench. • Place the light source in its carriage on the rail and set it at 0 cm. Lock it in place with the carriage base. • Place the recessed screen on a carriage and place it just in front of the light. Center the light beam on the screen. Department of Physics

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• Put the millimeter scale object in a carriage and position it at 10 cm. Move the recessed screen close to the object and adjust the object carriage until the center of its image is cast on the center of the screen. • Set the screen at roughly 100 cm. Mount the lens you are going to use on a carriage and place it between the object and the screen. Slide the lens back and forth between the object and the screen. The object's image center should remain at the center of the screen. • Place your lens at about 25 cm. Then slide the screen back and forth between the lens and the mid-point of the rail. The image should be centered for all positions. If it is, slide the screen to the end of the rail. The image should remain centered. You are now ready to make measurements with your lens. 2.3 Procedure 2.3.1 Convex lenses Focal Length Measure the focal length of the lens with each technique. Make sure to include uncertainties in values that you measure and to propagate them. Also, derive the formulas used in Bessel's and Abbe’s methods. (A) Simplest: Use the lens to form an image of the fluorescent lights on the floor. If you approximate the object distance as infinity, the distance between the floor and the lens is the focal length. (Have each person repeat three times per lens and take the average. The standard deviation is the uncertainty.) (B) Gaussian Lens Formula: Using the optical rail to mount all of the optics that you need, illuminate the gold object and view it on the recessed screen (see figure 1). Knowing the object distance, the image distance, and the Gaussian lens formula, 


1 1 1 + = 
 so si f 
 you can calculate the focal length of the lens. Repeat this measurement with two more object distances.

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Figure 1: Setup for Gaussian Lens Formula Department of Physics

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 (C) Autocollimation: Using the 500 µm pinhole as the source, place a mirror at the image. See Figure 2. When the source to lens (object) distance is equal to the focal length, the light that is reflected from the mirror and returns through the lens, should have the same diameter as the pinhole (see figure 3). Adjust the mirror so that the image of the pinhole from the mirror is very close to the pinhole. Move the lens until the image is as close to the size of the pinhole as possible. Measure the object distance. Repeat this two more times.




Figure 2: Setup for autocollimation

Figure 3: Beam path diagram for autocollimation. 
 (D) Bessel’s Method: If an object and its image are separated by at least 4 times the focal length of the lens, then there are two lens positions (for fixed object and image positions) that will result in images. One position will result in a magnified image and the other in a minified image. The focal length can be found by determining the distance between the two lens positions and using the following formula: f =

L2 − D2 , 4L

where L is a fixed distance from object to the screen (image), which must be greater than four times the focal length, and D is the distance between two positions of the lens that give focused images (see € figure 4). 
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Figure 4a: Setup for Bessel’s Method 
 
 






 Figure 4b: Magnified and minified images.


 
 
 (D) Abbe’s Method: Abbe's method is due to Ernst Abbe a German physicist and inventor. He made use of this method in the design of the Abbe Focometer. The description is taken from Pedrotti, Pedrotti, and Pedrotti’s Introduction to Optics. "An image of an object is formed on a screen by a lens. Leaving the lens fixed, the object is moved to a new position and the image screen moved until it again receives a focused image. If the two object positions are S1 and S2 and if the transverse magnifications of the images are M1 and M2 respectively, then:

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f =

S2 − S1 .” ( M11 − M1 2 )

Use Abbe's method to measure the focal length. See Figure 5. Although Pedrotti says to move the object to a new position when using Abbe's method, it is best to move the image, i.e., the screen, to a convenient place and then achieve€focus by moving the object then determining the object distance. 
 



 2.3.2 Concave Lenses

Figure
5
 





Focal length A concave (diverging) lens will not make a real image, so none of the above techniques are useful in measuring the focal length of a diverging lens. To measure the focal length of the diverging lens, use the lens labeled "diverging lens", then combine it with the converging lens that you studied in the first part of this lab. It is important to know that for this method to work the diverging lens must be weaker than the converging lens. If the two lenses are separated by a distance d, the combination will act like a converging lens of focal length:

1 1 1 d = + − f f1 f 2 f1 f 2 where f1 and f2 are the focal lengths of lens 1 and 2, respectively. Now use one (your choice) of the above techniques to determine the focal length of the doublet that you just formed, and from that € calculate the focal length of the diverging lens. Department of Physics

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2.3.3 Index of Refraction A spherometer is an instrument for the precise measurement of the radius of a sphere (such as a lens). See the pictures in the appendix. Read the instruction manual for the spherometer set and measure the radius of curvature of both sides of the two lenses that you studied. Using the measured radii, the previous measured focal lengths, and the lensmaker’s equation, 
 1 n 2 − n1 1 1 = ( − )
 f n1 R1 R2 
 determine the index of refraction of the lenses. How does this compare to the known values? (The lenses are made from BK7.) €

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Appendix
A
­
Items
used
in
thin
lens
experiments
 


Spherometer

Spherometer Kit




Gold Object

Pinhole

Optical Rail

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Millimeter Scale Object




Recessed Screen

Optical Carriage

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