Geometric Optics

Lab manual pp. 72-80

The extra credit assignment is at http://www2.hawaii.edu/~jmcfatri/labs/geomextracredit.html

Overview:

The goal of this lab is to:

verify the thin lens equation

determine the value of n, the index of refraction of our lens

Notes:

Introduction:

We will now move on to a subject which seems, on the surface, entirely different from what we have been studying in the previous experiments. The last two labs cover optics. This lab covers the thin lens equation, Snell's Law, and the lens maker's equation; the next, and last, lab covers refraction and spectroscopy. While you may not think that these ideas have anything to do with electricity and magnetism, you should remember that light is an electromagnetic wave, and hence, our understanding of optics is derived from a more general understanding of electric and magnetic fields.
Optics, in general, is quite complicated; it is a large field of research here at UH, both in the physics department and the astronomy department. What you are learning in class does not even stratch the surface. (If you don't believe me, ask yourself the following questions: why does light bend when going from one media to another? Why does it take "the path of least time"? Why do different materials have a different index of refraction? What properties change it? Why are some materials transparent and others opaque? What happens when I don't have a thin lens? What if I don't know the geometry of the lens? How could I model that? Why do computer screens only have three pixel colors (red-green-blue)? Why does RGB make all the colors I can see? -- I don't expect you to be able to answer any of these questions, but maybe you can ask your professor about them!)
Snell's Law:

Snell's Law is the following equation (it may use different symbols in your physics book):

n1* sin(theta1) = n2 * sin(theta2)

where n1 and n2 are indicies of refraction,
theta1 and theta2 are the angles the light ray makes to the normal of the interface surface.
(See Figure 1 in your lab manual)

Snell's Law is exact (there are no approximations used here). It implies that light will bend upon reaching a surface with a different index of refraction.

From there we want to see what will happen when we shine light through a lens.
First we will define the word focus. The focus is a point in space where all the light rays will converge (meet at a point) if the light came in from infinity (from a distance infinitely far from the lens).
Obviously what we have to do is solve Snell's law for every point on the surface in order to find out what the light does. Here we will use some approximations. We assume that:

the lens has a uniform index of refraction (bubbles, non uniform materials, etc. are not present)

the lens is thin

the angle at which the light is coming in is nearly parallel to the optic axis.

With these approximations we can introduce the lens maker's equation and the thin lens equation:
Lens maker's equation:

f = R / 2(n - 1)
where f is the focus, R is the radius of the lens. (This has the additional assumption that the lens is in air.)

and the thin lens equation: 1/s + 1/s' = 1/f We will attempt to verify the latter equation in our lab; the former equation we will use to determine n, the index of refraction of our lens.
Also we will look at the concept of spherical abberation.

Procedure:
Part I: Small aperture

You will need to obtain 5 holders, and one of each of the following: a light source (there are two kinds take either one), a green filter (if unavailable, pick another color), a small aperture, a lens (pick up by the edges!) and a white screen.

Place all of these in order on the optical bench, all at one end. Make sure they are aligned (all the centers line up).

Move the screen to the other end.

Move the lens and the aperture towards the screen until you see a sharp image

Record the distance from the light source to the lens (s), and the distance from the lens to the object (s').

Move the lens 5 cm towards the screen.

Move the screen until you see a sharp image.

Record the distance from the light source to the lens (s), and the distance from the lens to the object (s').

Repeat the last three steps until your screen gets to the end of the bench or the image gets too small to see distinctly.

Calculate 1/s and 1/s' for each data point and plot 1/s vs 1/s'.

Calculate fx and fy from the x- and y-intercepts. Find the average focus.

Determine R from the given equation (Equation 4, page 76). Use a caliper to determine w, d, and t.

Use the lens maker's equation to solve for n.

Part II: Ring aperture
Repeat Part I, except now use the ring aperture. Calculate the spherical abberation.
Discussion:
Please find all of the uncertainties listed in the Data Analysis on page 78.

Conclusion:
In addition to you normal conclusion, please answer the following questions:
Page 79, questions 1,2,3.