203-NYC-05: Waves, Optics & Modern Physics
Experiment # 5: Thin Lens
OBJECTIVE:
To verify the thin lens equation and the magnification equation for a thin lens.
INTRODUCTION:
The position and size of the image formed by a thin lens is related to the position and size
of the object by the following two equations:
1/p + 1/q = 1/f
m = yi / yo = - q / p
where: p = distance from object to lens
q = distance from image to lens
yo = object height
yi = image height
The following sign conventions are used:
positive p = real object
negative p = virtual object
positive q = real image
negative q = virtual image
positive f = converging lens
negative f = diverging lens
positive yi = upright image
negative yi = inverted image
Note: A negative magnification (for instance if p and q are both positive) means that the
image is inverted with respect to the object.
PROCEDURE:
1) Choose one of the converging lens from the set. Select a lens yellow-blue1. Find the
focal length of the lens by focusing the image of a distant object on a white card (e.g.
Daytime: the trees outside the window or the tower on H building; Nighttime: an ceiling
lamp in the corridor outside the lab). Repeat the measurement at least three times and
calculate the average and mean deviation.
2) Set up the object (illuminated box) on the optical bench. Mount the lens and the
screen on the bench; lens in between the object and the screen. Fix the distance lensscreen to 50.0 cm. Make sure that all three are vertical and perpendicular to the bench
axis. Start with the object as far as possible from the lens. Move it close to the lens until
a sharp image of the object is projected on the card. Measure the object distance with a
meter stick and estimate the uncertainty of this measurement. Move the object back and
forth to find the location of the sharpest image. Use a meter stick to measure the object
distance. Move the card back and forth again to locate the sharpest image and measure
1
Do not use either the red-yellow lens or the red-blue lens.
the object distance again. Repeat this procedure until you have at least three
measurements of the object distance. Calculate the average and mean deviation of
the object distance. Measure also the height and width of the image and the
corresponding dimension of the object. Estimate the uncertainty of these
measurements. Note whether the image is inverted or erect.
3) Move the lens closer to the screen to distances of 30cm 15cm and 12 cm and repeat the
procedure. For each pair p and q in 2) and 3) above calculate the value of (1/p + 1/q).
a) Are the results constant and do they agree with the focal length found for this lens?
b) From the measured image and object heights, calculate the lateral magnification
( m = yi/y0 ; sign – if the image is inverted) and compare with the corresponding
values of – q / p.
Work with averages and do not forget uncertainties.
4) Move the lens so that the object distance is about 2/3 of the focal length. Note that you
can no longer find an image on the white card. Remove the white card and look through
the lens to see the image formed. Is the image real or virtual? (You should now have 5
total object distances). Describe it and calculate its position.
5) Choose the diverging lens coded green from the set of lenses. Set up the lens about
30 cm from the object (illuminated box). Try to look for an image by placing a card on
the opposite side of the lens from the object and moving it through a large range of
possible image distances. Remove the card and look through the lens to see the image
formed. Is the image real or virtual?
ANALYSIS:
1) For the converging lens, draw to scale a ray diagram for the measurement done in part
4, (the one with the object inside the focal point of the lens). Draw a second ray diagram
for one of the cases with the object outside the focal point. In each case, use the focal
length as measured in the part 1 of the procedures. Measure the image distance and
magnification from each ray diagram.
2) Calculate the focal length of the lens. Use the lens equation along with the average
values for the object and image distances from each of the sets of measurements.
Calculate the ratios -q / p and yi / yo for each set of data.
3) Set up a table or several tables with all the measured and calculated quantities. Show a
sample calculation of all quantities and their uncertainties for one set of data. Pick one
where the uncertainty of the object (or image) distance is fairly large.
DISCUSSION:
1) In general where must the object be located for the image to be real? Where must the
object be located for the image to be virtual? When is the image upright and when
inverted? Discuss the two cases; convergent and divergent lenses.
2) Do the focal lengths calculated from the lens equation agree with each other and with
the focal length measured directly using a distant object?
3) Does the image distance found in the ray diagram agree with the measured value?
4) Are the ratios -q / p and yi / yo the same in every case?
5) Does the diverging lens form a real image?