Lens Maker Equation
Goal: Understand how lenses focus and image.
Lens Maker Equation:
1
𝑓
=
1
𝑠𝑜
+
1
𝑠𝑖
f is focal length, so is object distance, & si is image distance
Magnification: theory
𝑀= −
measurement
𝑠𝑖
M is magnification.
𝑠𝑜
𝑀= −
ℎ𝑖
hi is image height
ℎ𝑜
ho is object height
Objective 1. Test the lens maker equation.
Procedure: On the optics rail set up the components in the following order: light bulb, object
arrow, lens, imaging screen. Note that your object is the arrow, not the light bulb. Set the
object arrow somewhat close to the lens. Move the imaging screen back and forth to see if you
can create an image on it. If you cannot, move the object further away from the lens and repeat
the procedure until you get an image. Record the distance of the object from the lens, the
distance of the image from the lens, the height of the object, and the height of the image. Also
record the directions of the object arrow and the image arrow. Up is positive and down is
negative. After recording all information, move the object further away from the lens and repeat
your measurements. Do this for five different distances for each lens.
Repeat this procedure for a couple different lenses.
Analysis: For each lens, create a graph of
1
on the y-axis and
1
on the x-axis. From each
𝑠𝑖
𝑠𝑜
graph calculate the slope and y-intercept. The slope should be -1. The y-intercept is 1/f.
Calculate the focal length for each lens from the y-intercept.
For each pair of object and image distances, calculate the magnification from the heights and
the object & image distances. For each lens, graph magnification as a function of the object
distance. This will not be a straight line.
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Questions
1. Compare the focal lengths of each lens you measured. Describe how the geometry of the
lens (how much does it bulge) affect the focal length.
2. Compare the measured magnification of each lens to its focal length. For a given image
distance, what focal length give the biggest magnification?
3. How do the measured magnifications compare to the theoretical magnifications?
4. Where does an object that is far away from a lens focus? In this instance does the lens make
the image bigger or smaller than the object?
5. The lens system in the human eye can change focal length. The image distance always has
to be the width of your eye ball. Based on your experience with this lab, what is the focal length
of your eye when the object is far away?
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