Activity #7
The Refractive Index of Water

Grade Level: 9 - 12

Module: Visual Perception

Overview

When a light ray passes from one transparent medium to another, the it's speed and direction are altered. This phenomenon is known as refraction and is often thought of as the bending of light rays. It is boggling how many things in our lives are affected by this simple physical phenomenon-from the lenses inside all our eyes to the lenses in automobile headlights; from distortions in things seen through a glass of water to the photographed images in books and magazines. Refraction inherently causes problems for telescopes on Earth, since light passing from space through the Earth's atmosphere is subjected to variable of refraction. In fact, the primary reason for placing the Hubble space telescope in orbit around Earth was to eliminate this undesirable effect of Earth's atmosphere.

This activity aims to help students achieve understanding of refraction by allowing them to study the refractive properties of water. They make light rays pass from air to water and measure the angle of the incoming ray (the incident ray) and the angle of the exiting ray (the refracted ray). They find the mathematical relationship between the two angles, a relationship known as Snell's Law.

Key Question

• How does light behave when it goes from one clear medium into another?
• Can that behavior (refraction) be characterized mathematically?
• What does the refraction of light have to do with astronomical studies?

Time Frame:

Materials

• 2 protractors or 1 photocopy of the protractor (master below)
• water
• starch powder or milk
• flashlight and batteries
• black construction paper (about 6 cm square)
• tape
• black marker
• 1 half circular dish or a two-well petri dishes

• Photocopy of Data Tables 1 and 2

DATA TABLE #1

LIQUID TESTED:

DATA TABLE #2

LIQUID TESTED:

Getting Ready

Semi-circular plastic containers may be hard to obtain, whereas rectangular containers are more readily available in candy stores.

Glass containers create interference by their refraction.

A light sprinkle of starch powder or one drop of milk will make the beam more visible as it crosses the liquid medium.

Classroom Activity

1. Ask your students to recall any experience they have had with magnifying lenses. Ask, "What properties of a magnifying lens makes it magnify things?" One important aspect is its shape-a curved surface. The light is "bent" by the lens.) Ask the students to brainstorm and list all the things they encounter on a day to day basis that use lenses. (Some of the things volunteered in the Overview may be mentioned.) Once you feel that the class is beginning to appreciate the importance of lenses in their lives, tell them that they will be making some observations to understand the phenomenon underlying lenses-refraction.

2. Have the students work in teams with 4 - 6 students in each team. Distribute materials and have them set up the apparatus for measuring refraction as follows:
   a. Put a clear semicircular dish on top of the protractor. Line up the straight edge of the dish on the 90°-90° line
   b. Now half fill the container with water. If using a petri dish with two wells, fill only one of the wells.
   c. Place a circular piece of black construction paper over the flashlight head and tape it in place. The light should be well blocked. With a needle, make a pin-size hole through the paper.
   d. The flashlight is placed on the table toward the upper left quadrant of the protractor with the beam aimed toward the center of the protractor. Align the beam with one of the lines aiming toward the protractor center. It should make a spot of light on the container as it enters right at the center of the protractor.
   

3. Dim the room lights. Ask the students to observe that as the beam enters the water-filled container, it is bent-refracted. Tell the students to refer to the beam from the flashlight before it hits the dish as the incident beam. They can refer to the beam after it is "bent" as the refracted beam. It creates a spot of light somewhere on the curved part of the dish as it exits the container.
4. Instruct the students to position the flashlight at various angles for the incident beam, and observe the angle of the refracted beam. Distribute a Data Table to each student and have them record the values of the incident angles and the corresponding refracted angles in the Table.

Wrap-up Session

1. Prepare a line graph of the results from your corrected data. Incident angles are placed on the y-axis and refracted angles on the x-axis. Prepare the best straight-line plot based on the points. Based on the resulting graph, ask the students what patterns they can see? Is there a range of incident angles for which the refracted angles are very pronounced? For which range of incident angles is the refraction effect minimal?

2. Advanced students can calculate the sine for all incident and refraction angles collected for a respective liquid. If they plot the incident angle sine values on the y-axis and the refracted angle sine values on the x-axis, students can calculate the slope of their graph and derive the formula that relates incidence to refraction. The formula should be in the y = mx + b format taught in algebra classes. The slope is the index of refraction in Snell's Law, as given by the following equation:
   sin Øi ÷ sin Ør = constant (index of refraction).
3. Have a discussion about the properties of other clear objects, for example:
   The face plate of an astronaut's helmet-does it refract light?
   How does a prism make a rainbow?
   When a bear goes fishing, does the bear need to compensate for refraction of the image of the fish under the water?
   What causes near/farsightedness?

More Activity Ideas

1. Substitute another liquid in the same container and obtain incident and refraction angle data for this substance. Plot the results and compare the graph with that of water. Which substance gave a steeper line-graph? What relationship is there between the steepness of the line and the degree of refraction of liquids tested. Does there seem to be any relationship between the degree of refraction and the viscosity of the liquid?

2. Investigate the refractive ability of lenses. Students can investigate the relationship between lens curvature and focusing ability.

3. Have students research how solids and gases (or dispersed water droplets) might affect light by refracting it. Can light be affected by gravity? The unit of light is the photon. Does gravity act on these particles? (Yes) Do we observe gravitational effects on photons on Earth? (Not within the limits of our vision.) Where can we observe gravity acting on light? (Black holes!)

Background for Teachers

Prerequisites:

• Basic geometric principles
• Measurement of angles / use of a protractor

Vocabulary:

• Refraction - "bending" of light as it goes from one substance into another
• Angle of incidence - the angle between the light beam striking a surface and the line perpendicular to that surface
• Medium - a substance
• Light ray - a beam of light
• Angle of refraction - the angle that the refracted beam makes with the line perpendicular to the refracting surface
• Protractor - instrument for measuring angles
• Sine - a trigonometric function
• Snell's Law - a wave refracted at a surface makes angles relative to the normal to the surface, related by the equation
  ni sin &216;i = nr sin &216;r , where ni and nr are the refractive indices on each side of the surface

Skills:

• Physical measurement of natural phenomena
• Constructing and maintaining data tables
• Data comparison and analysis
• Designing effective scientific experiments

Concepts:

• Refraction of light
• Experimental models
• Scientific "law"

Keywords: Visual Perception, Refraction, Snell's law