Reflection: the bouncing of light off of a surface. The reflection can be diffuse (reflection angles are random as off of a rough surface) or specular (reflection angles are equal to incident angles as off of a mirror).
Refraction: the bending of light when a light beam passes at an angle to a surface between two optically transparent materials of differing densities.
Total internal reflection: when light passes from a more optically dense transparent material to a less optically dense transparent material, there is an internal angle beyond which the light is wholly internally reflected within the optically denser material.
During residential instruction, a demonstration on Monday included a laser, prisms, and half-round dishes with water to show bending of light.
Wednesday moved on to introduce convex and concave lenses. Use magnifying lens to produce an image. Introduce object distance and image distance. If sunny, a pinhole and paper punch hole camera can be used to demonstrate pin hole cameras and effect of aperture size on clarity. This was used to explain the human eye, iris, and pupil. The class traditionally went on to cover myopia, hyperopia, presbyopia, and remedies.
Another demonstration that fits here is the coin under the glass of water.
If a video was shown on Monday, Wednesday can be used to demonstrate reflection, refraction, and total internal reflection. Provide definitions. The class often watched Bill Nye the Science Guy - S02E07 Light Optics.
On a sunny Friday with a long enough, flat enough stretch of straight road, an inferior mirage might be visible and then explained.
Questions
Is there a linear relationship between the object distance and the image distance for a mirror?
Is there a linear relationship between the depth of an image below the surface of water and the actual depth of the object below the surface of water?
What is the index of refraction for water implied by that relationship?
Before breaking into groups and making measurements, ask the students to predict the relationship for the mirror. Label any theories by the last name of the student who first proposes the theory, "_________'s theory of reflection."
A focus on education: Note that while science tends to explore questions, these questions can be rewritten as student learning outcomes. Students will be able to determine the nature of the relationship between the object distance and image distance for a plane mirror. If the relationship is linear, students will be able to determine the slope and intercept for the relationship. Students will be able to determine the nature of the relationship between the object depth and image depth for am object underwater. Students will be able to calculate the index of refraction for water based on the slope of the relationship between the object depth and image depth for an object underwater.
There exists a mathematical relationship between the distance of an object in front of a mirror and the distance of the image "behind" the mirror.
There exists a mathematical relationship between the actual depth of an object and the apparent depth of an object seen below the surface of the water.
The word "image" is related to the word "imaginary." The image of the object is "not really there."
Image distance behind a mirror: index of reflection
Place an object in front of the mirror. Measure the apparent distance x₁ of the image of object "behind" the mirror. Measure the distance y₁ from the object to the mirror. Record the distances in centimeters. Note that to obtain a constant known as the index of refraction for water, the image distances will have to be placed on the x-axis and the object distances will have to be placed on the y-axis. This puts the independent variable on the y-axis and the dependent variable on the x-axis. For consistency, both of the two parts will record image distances as i and object distances as o.
i₁ o₁
[image distance] [object distance]
Where:
i1 is the image distance in centimeters
o1 is the actual object distance in centimeters.
When an object is underwater, the object appears closer. The actual depth of the object is called the object depth o₂ in this laboratory. Measure all distances from the top surface of the water. The object, especially when viewed from an angle above the water, will appear to be shallower that the actual depth y₂. This is an image of the object caused by refraction. Technically refraction is due to bending of the light as the light rays leave the water and enter the air. The apparent depth of the object under the water is the image depth i₂. To accurately determine the image depth you may have to move your head left and right above the object.
Image depth diagram
The diagram uses y₂ for the object depth o and x₂ for the image depth i.
Measure the object depth y₂ and the image depth x₂ for the object under the water. Start with an empty tub, recording both the object depth y₂ and the image depth x₂. Add water and repeat the measurements. Continue until the tub is full. Record the distances in centimeters. Other variables might be used in lieu of x and y during the laboratory session.
An alternate procedure is to use multiple beakers and graduated cylinders each with a different amount of water. This procedure has an advantage when the laboratory is done in locations where the water may go off during the day. Large graduated cylinders on the order of 50 cm tall tend to produce more accurate results.
Be careful to measure the actual and apparent depth below the surface of the water, not the top of the container.
Make measurements at many different depths. Run an mathematical analysis on the results, producing the appropriate graphs and mathematical relations.
x₂ y₂
[image depth] [actual object depth]
Where:
x₂ is the image distance in centimeters
y₂is the object distance in centimeters.
Graph: xy scattergraphs
Desmos is able to chart two data tables onto a single graph. If using spreadsheets to perform the analysis, then two charts are likely to be necessary.
Reflection analysis: If using Desmos and the data appears to be linear, determine the relationship between the image distance x₁ and the object distance y₁ using the relationship y₁~mx₁.
Refraction analysis: If using Desmos and the data appears to be linear, determine the relationship between the image distance x₂ and the object distance y₂ using the relationship y₂~nx₂.
For the apparent depth data, refraction theory suggests that the slope of the line should be equal to the index of refraction for water n. Look up the published index of refraction for water. Report this value and cite your source using either APA or MLA format. Run an error analysis to determine the percentage difference between the experimental index of refraction for water (the slope of the line on the second graph) and the published index of refraction.
Discuss the findings. Is there a mathematical relationship? Is the relationship linear or non-linear? Report a conclusion as to the relationship between the object distance and image distance for reflection in a flat mirror. If there are one or more mirror theories, discuss which one might be correct and why. Discuss the accuracy of your results for part two, the index of refraction for water. Discuss also any difficulties you encountered.
The lab will also be marked on grammar, vocabulary, organization, and cohesion.
Instructional note: Post-lab next day wrap-up could include refractive index of water and implication for divers working underwater. Relative distance and magnification. Alternatively, inferior mirages can be demonstrated if the conditions on campus, both physically and in terms of weather, permit the observation of mirages.