AP Physics 2 Lab – Lenses and Mirrors

Goal: The purpose of this experiment is to verify the expected properties and mathematical relationships for convex/concave mirrors and thin lenses.

Procedure Part A – Real Images
Throughout the experiment, measure object distance, image distance, object height, and image height using meter sticks and/or rulers.  For each converging lens and mirror project an image of a very distant object onto a screen.  Taking the object distance to be essentially infinite (do not need to measure), record the distance from the lens/mirror to the screen as the “measured focal length”.  Use an LED light source and each converging lens and mirror to create real images projected onto a screen.  Measure and record the height of the LED “object”.  Measure and record the distance to the image and the height of the image.  Vary the distance to the object to generate as wide a range of values as reasonably possible.  Produce three sets of data (two lenses and a mirror).   Each set should have at least 5 data points – preferably more.

Procedure Part B – Virtual Images
Use a diverging lens, which has a concave shape.  Using the LED source, you can confirm that there is no way to produce a real image projected onto a screen.  In this part of the experiment, you will simply look through the lens and assess the reduced size of the virtual image that it produces.  The “object” in this case will be a grid of squares (4 or 5 per inch).  Place the grid of squares at each of the given object distances and then position your eye at the same distance on the opposite side of the lens. (i.e. The lens is located at a point precisely halfway between your eye and the grid of squares.)  Compare the squares seen through the lens to the squares on the grid as seen without the lens.  You should arrange the grid, lens, and your eye so that you can see the grid without lens and the image of the grid “side by side” simultaneously.  Then determine the apparent magnification by counting squares – for example, if ten of the squares in the virtual image appear to be the same size as two and a half squares as seen without the lens, then the image’s squares appear one fourth as wide and the apparent magnification is:  2.5/10 = 0.25.

Analyses and Interpretations

1. Use the blank columns in the data table to calculate and record values that can be used to produce a single high-quality linear graph that illustrates the relation between object distance and image distance.  Plot data from both the lens and the mirror and include a key, using different symbols and/or colors to distinguish the two data sets.  Determine and include a linear regression equation and line of best fit for each data set. 

2. Create a high-quality graph of height of image vs. object distance.  Plot data for both the lens and the mirror and include a key, using different symbols and/or colors to distinguish the two data sets.  For each set determine a curve of best fit with equation of form:   .

3. Create a high-quality graph of object distance vs. the reciprocal of the apparent magnification for the data collected using the diverging lens.  Determine and include a linear regression and the line of best fit.

Questions

1. Explain whether, and how, your data, graphs, etc. support or refute the expected properties of lenses and mirrors.  Be specific.

2. Consider the linear regressions from the first graph.  (a) Use one of the coefficients from each equation to calculate the focal length for each lens and the mirror.  Show your work.  (b) Discuss the significance of the other coefficient – is it what you would expect?  Explain.

3. Consider the curve fit equations for the second graph.  The coefficients A and B can be used to determine focal length and object height.  (a) Derive an expected relationship for this graph: an expression for h_i in terms of d_o, h_o, f, and any appropriate constants.  Show your work.  (b) Use the coefficients A and B to calculate focal length and object height for each data set.

4. Consider the linear regression for the data from Part B – the diverging lens.  The slope of the line should equal twice the absolute value of the focal length and the y-intercept should equal twice the focal length.  (a) Determine the focal length using the slope.  Show work.  (b) Determine the focal length using the y-intercept.  Show work.  (c) Optional challenge:  show why these calculations work!  The apparent magnification is the product of two factors.  The lens formula  gives the ratio of the sizes of image and object.  But when you view an object (or an image!) from a certain distance it has an effect on how big it looks.  For example, if you move twice as far from an object it will appear half as big when viewed from that distance.  This additional “magnification factor” is simply the ratio of the two distances.  In this experiment it is the ratio:  M ʹ = (distance from your eye to the grid)/(distance from your eye to the virtual image).  Then the apparent magnification is the product:  M∙M ʹ.

5. Determine percent error and/or deviation for each data set .  There are different ways that this might be done – it is your choice!  Just make it clear what you have determined and show your work.

6. Discuss error.  This means you should point out specifically any signs and/or evidence of error apparent in your results.  And you strive to explain the sources of error that might account for the observed imperfections.

A completed report consists of the following (in this order):

· Completed data/observations tables

· Linearization graph for image distance and object distance, with lines of best fit and equations

· Graph of image height vs. object distance, with curve fits and equations

· Graph of object distance vs. reciprocal apparent magnification, with lines of best fit and equations

· Answers to questions

Data/Observations

Part A – Real Images

Convex Lens
Object Height:		Measured Focal Length:
Object Distance (cm)	Image Distance (cm)	Image Height (cm)

Concave Mirror
Object Height:		Measured Focal Length:
Object Distance (cm)	Image Distance (cm)	Image Height (cm)

Part B – Virtual Images

Concave Lens
Object Distance (cm)	Distance Lens to Observer’s Eye (cm)	Apparent Magnification	Reciprocal of Apparent Magnifcation
45.0	45.0
40.0	40.0
35.0	35.0
30.0	30.0
25.0	25.0
20.0	20.0
0.0	0.0	1.00	1.00