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Chapter 10
Thin Lenses
Name: Lab Partner: Section:
10.1 Purpose
In this experiment, the formation of images by concave and convex lenses will be explored. The application of the thin lens equation and the magnification equations to single and compound lens systems will be investigated.
10.2 Introduction
10.2.1 The Thin-Lens Equation
Lenses are common optical devices constructed of transparent material e.g. glass or plastic, which refract light in such a way that an image of the source of light is formed. Normally, one or both sides of the lens has a spherical curvature. When parallel light from a source impinges on a converging lens, the parallel rays are refracted so that all the light comes together at a focal point. The distance between the lens and the focal point is called the focal length of the lens. An imaginary line parallel to the light rays and through the center of the lens is called the principal axis. See Figure 10.1. Another basic type of lens is the diverging lens. With a diverging lens, parallel rays are spread out by the lens. The focus of a diverging lenses is on the same side of the lens as the impinging parallel rays. See Figure 10.1. The thin-lens equation relates the distance of the object from the lens, d (^) o , and the distance of the image from the lens, d (^) i , to the focal length of the lens, f. See Figure 10.2. The thin lens equation is: 1 d (^) o
d (^) i
f
The magnification equation is:
m =
Image Height Object Height
h (^) i h (^) o
d (^) i d (^) o
Figure 10.1: Converging lens (left) and diverging lens (right).
ho
hi
f
do di
Figure 10.2: Geometry for the thin lens equation.
where h (^) o is the object height and h (^) i is the image height. The magnification, m, is the ratio of these heights. Since the triangle formed by the ray through the center of the lens and the object distance and height is a similar triangle to the triangle formed by the ray through the center of the lens and the image distance and height, the ratio of (^) hh (^) o^ i = - (^) dd^ i (^) o. The following sign conventions are used with the thin-lens and magnification equations:
- f is positive (+) for a converging lens. f is negative (-) for a diverging lens.
- d (^) o is positive (+) when the object is to the left of the lens (real object). do is negative (-) for an object to the right of the lens (virtual object).
- d (^) i is positive (+) for an image formed to the right of the lens for a real object. di is negative (-) for an image formed to the left of the lens for a real object.
- m is positive (+) for an image that is upright with respect to the object. m is negative (-) for an image that is inverted with respect to the object.
When more than one lens is used, the thin lens equation can be applied to find the image location for the first lens. This location of the image from the first lens is then used as the object for the second lens and a second application of the thin lens equation. This process will be used in the last part of the experiment to investigate a concave lens. For the magnification equation for multiple lenses, the total magnification is the product of the magnifications of the individual lenses.
Light Source
Target Lens 75mm^ Screen
Cross Arrow
Figure 10.5: Arrangement of components for the approximate focal length measurement for a single lens.
the image, which will be very small, being at the focal length of the lens.
- Place the white viewing screen at the far end of the magnetic optical rail. Place the cross arrow on the light source at the other end of the rail.
- Place the 75 mm (0.075 m) convex lens on a magnetic holder at the far end of the magnetic optical rail near the screen (see figure 10.5). The lens should be centered on the opening in the holder.
- Adjust the lens until a sharp very small image is formed. Since the object i.e. the cross arrow target is far away, the distance between the lens and the screen is approximately the focal length of the lens. Record the distance between the lens and the screen.
Distance between the lens and the screen (d (^) i )
- The distance between the object (cross arrow target) and lens ( (^) d^1 0 ) is not infinite. Measure and record the distance between the object and lens and record the value.
Object distance (d 0 )
- Using the thin lens equation calculate the focal length of the lens. Show your calculation below and calculate the percentage error with the given focal length (75 mm) of the lens.
Focal length of lens % error
10.3.2 Procedure for the Focal Length of a Single Convex Lens
The magnetic optics rail contains a measuring scale along the side. The optics components mount on magnetic component holders. Each holder has a small indicator position on the side to locate the position of the component on the rail side scale (see Figure 10.4). Each component should be centered on the holder.
- Attach the cross arrow target (CAT) to the front of the light source. Place the light source at one end of the rail. Place the 75 mm (0.075 m) focal length lens on a holder and position it 30 cm (.3 m) from the CAT. See Figure 10.6.
- Calculate the location of the image formed by the lens using the thin lens equation. Calculate the size and orientation of the image using the magnification equation. Show your calculations below and record the values.
Calculated image distance d (^) i Calculated magnification Orientation
- Place the view screen on a holder and place it at the calculated image position. Make small changes to the screen position to get a good focus.
- Record the measured object and image positions for your lab report. Measure the image size and orientation. (The circle on the CAT is 1 cm in diameter. Slide the edge of viewing screen to the middle of the image to use the scale on the viewing screen for an accurate measurement of the size of the image.) Calculate the percentage di↵erence between the calculated and measured values.
Measured image distance d (^) i % di↵erence between calculated and measured d (^) i Measured magnification % di↵erence between calculated and measured magnification
- In the thin lens equation, the sum of the inverses of the object distance and image distance are equal to the inverse of the focal length. If the image and object distance are interchanged, another image should be observed on the screen assuming the total distance between object and image is not changed. Move the lens so the distance be- tween the screen and the lens is 30 cm (.3 m). Is a sharp image formed by interchanging the object and image distance? What happens to the magnification?
Light Source
CAT
concave convex −150 mm75 mm
.1 m^ .1 m
Screen
Figure 10.7: Compound lenses: The -150 mm focal length concave lens is placed in front of the 75 mm convex lens.
10.3.4 Questions
- Explain why it is di cult to view a virtual image.
10.4 Conclusion
Write a detailed conclusion about what you have learned. Include all relevant numbers you have measured with errors. Sources of error should also be included.
