Materials

Optics Bench with table, protractor and light source

Pasco Ray Optics Kit

Semicircular Cylindrical lens

Paper

Ruler

Introduction

In this activity we will determine the relationship between the incident and refracted light at the boundary between air and glass. The relationship we will observe is called Snell's law after a Dutch scientist who described it in the 17^th century. This law has been known for much longer, however. Ptolemy of Alexandria actually had tabulated data in his book The Almagest in the 2^nd century AD, and the law was described by Islamic scholars in the middle ages.

Part 1 Snell’s Law

Procedure

1. Set-up

Adjust the mask on the light source so that a single ray comes out which hits the center of the protractor on the optics table. Adjust the protractor on the optics table so that 0° mark paces the light source. Place the semicircular cylindrical lens with its flat side facing the light source and so it is aligned along the axis of the protractor.

2. Data acquisition

Align the ray box so that the light hits the center of the protractor. Determine where the beam exits the lens. Record the incident and refracted angles in the data table below. Be sure to measure both angles from the normal. Determine the sine of the incident and refracted angles and record that value in the data table as well.

3. Repeat the Procedure

Rotate the table by 10° and repeat the procedure. Make sure that the incident ray hits the center of the protractor each time. You may have to apply a push slightly on the light source to obtain this. Record the incident and refracted angles and their sines in the data table. Repeat the procedure increasing the incident angle by 10° each time until reaching 80°. Record your data in the table below. Make sure that the incident and refracted angles are measured from the normal.

Data Table

Incident Angle, q_i	sin(q_i)	Refracted angle, q_r	sin(q_r)

Data Analysis and Questions

Q1) For your first data point, the incident light was normal to the glass. Did the light bend in the glass?

Q2) In general if light is normal to an interface what will be its refracted angle?

Q3) Why is it important in this procedure that the piece of glass was semicircular? (Hint: Does the light bend when it exits the glass?)

Use whatever software you like to make a correctly labeled graph of the refracted angle vs. the incident angle. Add a regression line.

Q4) Do your data appear to lie on a straight line? Hint: it probably will for the smaller angles, but does anything happen at the larger angles?

Plot a properly labeled graph of the sine of the refracted angle vs. the sine of the incident angle. Add a regression line.

Q5) Do these data appear to lie on a straight line? In particular for the larger angles is it a better fit than the previous graph?

The result you have observed is called Snell's law. It describes the relationship between incident and refracted angle and is given by n_isinq_i = n_r sin q_r where n is the index of refraction of the light in that medium. The index of refraction gives the speed of light in that medium as v = c/n, where c is the speed of light in vacuum c = 3.0 x 10⁸ m/s.

Q6) Given the definition of the index of refraction in the previous sentence, what are the units of the index of refraction?

Q7) Use your second graph to determine the index of refraction of the glass. Record your result.

Q8) Determine the speed of light in the glass that we used. Record your result.

Part 2Refraction by Lenses

Procedure and Questions

Adjust the mask in front of the light source so that you obtain five parallel rays. Remove the semicircular cylindrical lens and place the white piece of paper on top of the optical table. Place the biconvex lens in front of the rays on top of the white sheet of paper. Trace the incident and refracted rays on the paper using a straight edge.

Q9) Sketch how the rays look.

Q10) Do the rays seem to come to a focus? If so determine the focal length.

Reverse the orientation of the lens.

Q11) Do the rays behave the same regardless of orientation of the lens?

Q12) Measure the focal length of the lens in this orientation. Is it the same as before?

Replace the biconvex lens with the biconcave lens.

Q13) How do the rays passing through the biconcave lens compare to those passing through the biconvex lens?

Q14) Fill in the following blanks with either diverging or converging. A concave lens produced _________________ rays, and thus a concave lens is also known as a ____________________ lens. A convex lens produced _________________ rays, and thus a convex lens is also known as a ____________________ lens.

Using a straight edge, trace the incident and refracted rays on the white piece of paper. Backtrack the rays passing through the biconcave lens.

Q15) Do the backtracked rays appear to come together at a point?

Q16) Determine the focal length of the biconcave lens.

Reverse the orientation of the lens.

Q17) Do the rays behave the same regardless of orientation of the lens?

Q18) Measure the focal length of the lens in this orientation. Is it the same as before?

You should have noticed that a lens has the same focusing properties if it is reversed. We describe this property of lenses by saying that they have two focal points. One in front of the lens and one behind.

Q19) Sketch a diagram of a converging lens and indicate its front and back focal points.

Q20) Sketch a diagram of a diverging lens and indicate its front and back focal points.

Q21) Notice that concave lens like a convex mirror diverged parallel rays incident on it. What is the sign of the focal length of a convex mirror?

Q22) By analogy, what should be the sign of the focal length of a concave lens?