Physics 103

**Geometrical Optics**

The mathematical model of geometrical optics says light travels in straight rays, except at interfaces, where the rays may bend. A luminous point is the source of rays going in all directions, and if some of them eventually intersect again, through being deviated by lenses, mirrors, etc., the intersection point is an image of the original object. There is nothing obvious about this, and it may not even be clear what it means in all cases. The aim of this lab is to connect this mathematical model to real phenomena. We will

(1) Build a model of the eye

(2)
Check the relationship between object position *o* and image position *i* for a lens

(3) Construct two kinds of telescopes

(4) Construct a microscope

The optical benches we will use are just meter sticks mounted on feet, with lens holders that can slide on them. Notice the square notch on one side of each lens holder. If you put this notch on the side where the meter stick is ruled, you can easily read the position of the center of the holder, which coincides with the post, which more or less coincides with the position of the lens. This is how we will determine the positions of optical elements.

**Model
of the eye**. Mount a suitable
convex lens and a white screen so that images of distant objects form on the
screen. The objects will have to be
quite bright to show up. During the day,
the scene out the window is the best source of bright objects. At night we will have to use lamps on the
other side of the room. Try two
different lenses for the model eye. How
does the image size depend on the size of the model eye (i.e., the distance
between lens and retina)? How does the
brightness of the image depend on size?
Why is this?

**Object and Image**. Mount a small light on the optical bench and
use a convex lens to form an image of this (nearby) object on a screen. A good focal length for the lens would be about
20 or 30 cm. Slide the elements around
and find different positions that produce sharp images of the light on the
screen. (In recording the positions, be
sure to take account of the fact that the light is not at the location of its
post, but is rather significantly displaced along the optical bench).

Enter the data into a table in Excel, and by subtracting
find the quantities *o* and *i* that give the
object and image positions relative to the lens. Recall that *o* is the distance of the object upstream from the lens, and *i* is the distance of the image downstream from the lens. From geometry we expect

_{}

Here *f* is
the focal length of the lens.

This says that 1/o should be a linear function of 1/i. Plot these quantities in Excel, and if indeed there is a linear relationship, make sense of the slope and intercept. Refer to the handout on Excel about how to do arithmetic in data tables, and how to plot, fit, etc.

**Telescopes**. Mount a long focal length convex lens on the
optical bench. Behind it there must be a
real, inverted image of distant objects in front of it. Get back behind it by much more than the
focal length and try to see this real image, as if it were hanging in
space. Approach it with your eye and
note when you have gotten too close to see it clearly.

Once you know where the real image is, approximately, put in a second convex lens, of shorter focal length, as an eyepiece to help you see the real image from close up. Why is the total length of the telescope the sum of the focal lengths? What is the magnification, very roughly, and how does it compare to what you would expect from the focal lengths? (You can estimate the magnification by keeping both eyes open, comparing the image you see through the telescope with the one you see unaided.)

Also try using a concave eyepiece, to form a Galilean telescope. Answer the same questions as before.

**Microscope**. Use the same strategy as before, now to look
at something close up. As before, choose
an objective lens, this time with as short a focal length as possible, and put
it a bit more than a focal length from a suitable object. Find the magnified, inverted image in space
behind it. This may take considerable
fiddling around. If the image you see is
not inverted, it is not the one you are looking for! Once you know where the real image is, add a
suitable eyepiece. Since our lenses are
not the very short focal length lenses that would make truly powerful
microscopes, your microscope will superficially not resemble the familiar
microscope, but its operation will be exactly the same. What magnification can you achieve?

Geometrical Optics worksheet: use the questions above as a guide to writing an expository paragraph about each item, with relevant sketches to aid the exposition.

(1) Model of the Eye

(2) Object and image:

Data table: Sketch of graph:

Interpretation: what do the slope and intercept mean? What is the uncertainty?

(3) Telescope

(4) Microscope

OPTIONAL: if you wish, please say what you liked or didn’t like about this lab, and how it might be improved.