Lenses- effects of curvature, materials on light beams

Introduction: (Initial Observation)

Lenses have many practical uses in science, medicine and industry. They are used in simple magnifiers, cameras, microscopes, telescopes, eye glasses, eyes themselves, and many other devices. Our objective in this project is to study the effect of curvature and material on light beams. we want to know if two same size lenses will act the same if they are made from two different type of material. We also want to know how does the curvature affect the properties of a lens? Image

The results of this study may be used in designing better optical devices such as telescopes and cameras.

Dear

This project guide contains information that you need in order to start your project. If you have any questions or need more support about this project, click on the “Ask Question” button on the top of this page to send me a message.

If you are new in doing science project, click on “How to Start” in the main page. There you will find helpful links that describe different types of science projects, scientific method, variables, hypothesis, graph, abstract and all other general basics that you need to know.

Project advisor

Please note that this page is really describing two different projects you may choose from. One project is the study of curvature and the other is the study of materials.

When you study the effect of curvature, you will learn how does the curvature affect the light beam. This will help you choose the lenses for your new designs of optical instruments (microscope, telescope, camera) or modify a lens in order to change an existing design. You may also learn how to combine lenses in order to get specific results.

When you study the effect of materials, you will learn how does changing the lens quality affect your design. For example you will know what will happen if you remove a glass lens from your camera and replace it with an acrylic lens with the same physical size.

At this time you must select if you want to study the effect of curvature or the effect of materials on light beams.

How do we measure changes on light beam?

Lenses refract the light beam and collect them in a spot called focal point. Focal distance is the distance of focal point to the center of the lens. Focal distance is a measurable value that represent how the light is refracted by the lens. Everyplace in this project where you need to say “the effect on light beam”, you can say “the effect on focal distance” instead.

Information Gathering:

Find out about lenses and their properties. Read books, magazines or ask professionals who might know in order to learn about the effects and applications of lenses. Keep track of where you got your information from. Following are some general information that you may find.

A lens is a device for concentrating or diverging light, usually formed from a piece of shaped glass. The term lens is also used for analogous devices used with other electromagnetic radiation; for instance a microwave lens can be made from paraffin wax.

In its usual form, a lens consists of a slab of glass or other optically transparent material. with two shaped surfaces of a particular curvature. It is the refractive index of the lens material and the curvature of the two surfaces that give a particular lens its particular properties. A lens works by refraction (bending) the light that passes through it, in a similar manner to a prism.

A concave lens is thin in the middle compared to its edge.
A convex lens is thick in the middle compared to its edge.

Following are some helpful links about lenses:

http://cvu.strath.ac.uk/courseware/msc/jbaggot/lenses/lenses.html

http://courses.washington.edu/cerobert/116A/LectureNotes/ICP21/6ConvergingLenses.pdf

http://www.encyclopedia.com/printablenew/07365.html

http://acept.la.asu.edu/courses/phs110/course_info/class_notes/fall2001/l&o-lens.pdf

http://www.phys.ufl.edu/~deserio/simplens/simplens.htm

Example of lens making problems:

. A plano-convex lens having a focal length of 25.0 cm is to be made with glass of refractive index 1.520. Calculate the radius of curvature of the grinding and polishing tools to be used.

The necessary radius of curvature may be found from the lens maker’s equation

1 /f = (n2-n1)/n1 * {(1/R1) – (1/R2)}

where here n1=1 since the surrounding medium is air, and 1/R2=0, since the plane side has infinite radius of curvature. Thus the radius of the first side is

R 1 =(n -1)f = (1. 520 -1)(25. 0cm )=13. 0cm.

Question/ Purpose:

What do you want to find out? Write a statement that describes what you want to do. Use your observations and questions to write the statement.

This project has two parts and each part can be a separate project.

For the first part where you study the effect of curvature on light beams, you may start with a question like this:

How does the curvature of a lens affect the focal length?

How does lens thickness affect the focal length of a convex lens?

Changes in the curvature and focal point also affect the magnification of images by a lens. Seeing an object depends on how our eyes receives the light from the object. Having the light, reflected from the object, pass through a lens placed between the object and our eyes affects the appearance of the object based on the curvature of the lens. So, you could also have a question like “How does the curvature of a lens affect the magnification?”, the problem is that magnification is not easily measurable.

For the second part where you study the effect of lens material on the focal point, you may start with a question like this:

How does the lens material affect the focal length?

In other words we want to know if two lens with the same size and curvature are made of two different types of material will have the same focal length and refraction properties?

Identify Variables:

When you think you know what variables may be involved, think about ways to change one at a time. If you change more than one at a time, you will not know what variable is causing your observation. Sometimes variables are linked and work together to cause something. At first, try to choose variables that you think act independently of each other.

This is how you define variable where you study the effect of curvature on light beam:

Independent variable (also known as manipulated variable) is the curvature. Curvature may be expressed as the the radius of the lens curve in one side (assuming that both sides have the same curvature). You may simply take the direction of curvature as a variable and have values such as (Bi-Convex, Plano-convex, bi-concave, plano-concave, convex-concave)
Dependent variable (also known as responding variable) is the focal length of the lens.
Constant is the light source
Controlled variable is the temperature.

This is how you define variable where you study the effect of lens material on light beam:

Independent variable (also known as manipulated variable) is the lens material. Possible values are glass, acrylic, polycarbonate, silicon,..
Dependent variable (also known as responding variable) is the focal length of the lens.
Constant is the light source
Controlled variable is the temperature.

Note that controlled variable is not the same as control experiment.

Hypothesis:

Based on your gathered information, make an educated guess about what types of things affect the system you are working with. Identifying variables is necessary before you can make a hypothesis.

Following are some sample hypotheses.

A lens that is thin in the middle (concave) will make objects look smaller and a lens that is thicker in the middle (convex) will make objects look larger. By increasing the curvature, concave lens will make the objects look smaller and the focal length will be larger (remember -2 is larger than -3), but convex lens will make the objects look larger and focal length will become smaller.

For the second part of the project, if identical shape and size lenses are made of different material, they will not have different focal points because the light beam that bends when entering the lens will bend again in an opposite direction when exiting the lens and this will void the effect of refraction index on lens.

Experiment Design:

Design an experiment to test each hypothesis. Make a step-by-step list of what you will do to answer each question. This list is called an experimental procedure. For an experiment to give answers you can trust, it must have a “control.” A control is an additional experimental trial or run. It is a separate experiment, done exactly like the others. The only difference is that no experimental variables are changed. A control is a neutral “reference point” for comparison that allows you to see what changing a variable does by comparing it to not changing anything. Dependable controls are sometimes very hard to develop. They can be the hardest part of a project. Without a control you cannot be sure that changing the variable causes your observations. A series of experiments that includes a control is called a “controlled experiment.”

Experiment 1: Effect of lens curvature on light

Introduction: In this experiment we use a water lens to test the effect of curvature direction on light.

Material:

Metal washer
Petroleum jelly
Small plastic cups
Microscope slide
Eye dropper
Lens Investigation Report Form (for each student)
Tap water
Printed page such as newspaper

Procedure:

1. Turn the 2 small plastic cups upside down on the newspaper page. Bridge the slide across the 2 cups, about 1cm of the narrow end of the slide overlaps each cup. Spread a thin layer of petroleum jelly on the bottom of the washer and place the washer (jelly side down) on the center of the slide between the 2 cups.

2. Observe the newsprint on the newspaper page through the hole in the center of the washer and record observations.

3. Add 2 or 3 drops of water to the hole in the center of the washer and spread the water around inside the hole. This produces a concave lens.

4. Observe the newsprint through the hole in the center of the washer and record observations.

5. Add 2 or 3 more drops of water to the center of the washer so that the water heaps higher than the washer. This produces a convex lens.

6. Observe the newsprint through the hole in the center of the washer and record observations.

Observations/Data/Evidence (charts, graphs, tables):

With a water lens you cannot measure the curvature and focal point. To be able to do measurements you must use real lenses. The following procedure is an alternate method using real lenses. You will need a set of lenses with the same outer diameter and different curvature.

Alternate experiment

Effect of lens curvature on light (using a lens set)

Materials: Set if lenses with identical outer diameter and different curvature.

Procedure:

On a large white paper draw curves (part of a circle) with diameters of 2cm up to 60 cm. All with the same center. Number all curves with their radius.

For each lens in your collection measure the curvature of the lens. To do this align the side of the lens to different circles and find the closest curve to your lens. The radius of that circle is the curvature of your lens.

Measure the focal length of each convex lens directly by obtaining the image of a very distant object (sun, moon, stars) on the screen. measure the distance from the center of the lens to the focused image in millimeters.

Measure the focal length of each concave lens directly by obtaining the image of sun on the screen. When the diameter of the sun image is double the diameter of the lens, then the distance from the center of the lens to the image has the same value as the focal point; however, the focal point of concave lenses are negative. For example of the distance is 200mm, then the focal point is -200mm.

Record the results in a table like this:

Lens type	Curvature (radius)	Focal point

Experiment 2:

Introduction:

In this project we want to see the effect of curvature on the focal length of a lens. This information can be used in designing cameras and other optical devices that need to focus on an image.

Need to know:

Hold the lens so that a light from an object across the room or outside a window can pass through the lens. The distance from the object to the lens is called the object distance. Place a sheet of white paper on the other side of the lens and move the paper closer to or farther from the lens until you are able to see an image of the object focused on the paper. Measure the distance from the lens to the paper. The distance from the lens to the image is called the image distance and if the object distance is large, the image distance is very close to the focal length of the lens. When the object is infinitely far away from the lens, the image distance will be exactly equal to the focal length. These terms and ideas should be familiar to you. Their meaning is the same as for mirrors. When the object distance is not infinitely far away, the image will not be located at the focal point but at some other location.

Materials

meter stick
plasticine (or hot melt glue)
convex lenses of various thickness
calipers Or micrometer
white paper screen

Safety Precautions

handle glass lenses carefully.

Procedure:

1. Using plasticine (or hot melt glue), mount a lens over the meter stick ruler (see diagram).

2. Point the lens at a distant object (e.g., window or a candle or flashlight).

3. Move the screen back and forth until the image is clearly focused.

4. Measure and record the distance between the lens and the screen.

This distance is the focal length (f) of the lens.

5. Measure and record the curvature of the lens (as described in experiment 1, alternate procedure). Convex lenses with the same outer diameter often have a higher curvature if their thickness in the center is more.

6. Repeat steps 1 to 5 for 3 or 4 different lenses.

Observations:

Trial Number	Curvature *	Focal Length (f) cm
1
2
3
4

* Instead of curvature you may write the thickness of the lens in the center in millimeters.

In your report write:

How does the focal length change as the curvature in a double convex increases and the lens becomes thicker in the center?

Which convex lenses have a shorter focal length? Thicker ones or thinner ones.

Experiment 3:

Introduction: In this experiment we want to see how does the type of material affect the light beam going trough a lens. To do this we will make two lenses, one from water and the other from mineral oil and compare the results.

Material:

4 Watch glasses
Glue gun (hot melt glue)
Pipette or straw
2 Rulers
Some nails or match sticks to be used as spacer.

Watch glasses available at MiniScience.com part # GW75 and GW100

Procedure:

Place two watch glasses over each other to form a convex lens structure. You need to seal them together to form a lens. Before sealing them together at the outer rim, use spacers such as match sticks between two watch glasses in a few spots around the rim of the lens so that a space of a few millimeters is created between two watch glasses.

Spot glue the watch glasses such that they hold steadily. Remove the match sticks and complete sealing the watch glasses, except for about two cm opening that will be used to fill up the lens with liquids. Use glue to secure the lens (opening up) on a ruler or a piece of wood. Prepare another lens just like this one and fill them up one with water and another one with mineral oil. These are the two lens that you need to compare together.

Last Minute Change: After filling half of the first lens up with water, you may want to change your plan and fill another half up with mineral oil. Mineral oil does not mix with water and in this way you will have a lens, half with water and another half with mineral oil.

That is what we did in this picture. We even did not have to measure the focal length to see the difference. Each half had a different magnification that could only be attributed to the type of material.

Since our lens is filled with liquid and we can not simply modify it’s orientation, we measured it’s focal point at night by making a setup similar to experiment 2.

We place the light source about 30 feet away. By moving the screen back and fourth we can find the image (focal point) when then screen is about 10 to 20 cm away from the lens (depending on our lens, it may be higher or lower).

Materials and Equipment:

List of material can be extracted from the experiment section.

Results of Experiment (Observation):

Experiments are often done in series. A series of experiments can be done by changing one variable a different amount each time. A series of experiments is made up of separate experimental “runs.” During each run you make a measurement of how much the variable affected the system under study. For each run, a different amount of change in the variable is used. This produces a different amount of response in the system. You measure this response, or record data, in a table for this purpose. This is considered “raw data” since it has not been processed or interpreted yet. When raw data gets processed mathematically, for example, it becomes results.

Conclusion from Experiment 1:

Type of Lens	Appearance of Print
No lens	Actual Size
Lens 1	Smaller
Lens 2	Larger

Conclusion from Experiment 2:

Write what is the relationship between the thickness of a lens and its focal length?

Conclusion from Experiment 3:

Write the difference between a water lens and oil lens.

With a lens that is half water and half oil, we could not get a clear focal point, so once we covered one half with a black paper and measured the focal point. Then we covered another half and measured it again.

Focal length of mineral oil lens was smaller than focal length of water lens.

Calculations:

Description

Summary of Results:

Summarize what happened. This can be in the form of a table of processed numerical data, or graphs. It could also be a written statement of what occurred during experiments.

It is from calculations using recorded data that tables and graphs are made. Studying tables and graphs, we can see trends that tell us how different variables cause our observations. Based on these trends, we can draw conclusions about the system under study. These conclusions help us confirm or deny our original hypothesis. Often, mathematical equations can be made from graphs. These equations allow us to predict how a change will affect the system without the need to do additional experiments. Advanced levels of experimental science rely heavily on graphical and mathematical analysis of data. At this level, science becomes even more interesting and powerful.

Conclusion: (include reasons for your conclusion)

Using the trends in your experimental data and your experimental observations, try to answer your original questions. Is your hypothesis correct? Now is the time to pull together what happened, and assess the experiments you did.

Sample Conclusion from Experiment 1:

Changing the shape of the lens affected the size of the image seen. The first lens created (concave lens) caused the newspaper print to appear smaller. By adding more water the second lens (convex lens) was created. This lens caused the newspaper print to appear larger.

Conclusion from Experiment 2:

To come up with a conclusion for experiment 2, answer these questions after your experiments:

In a similar material (e.g., glass, plastic), how does one change the focal length?
What type of lens is in the human eye? Explain.
In the human eye, the retina acts as a screen where the image appears. Both the eye’s lens and the retina are in fixed positions (can’t be moved). In order to see a close object the focal length has to be shortened and, in order to see a more distant object, the focal length has to be lengthened. How, then, is the eye able to focus on any object regardless of distance?
A farsighted person is unable to see clearly objects that are close because the focal point is “behind” the retina. What type of lens would be used in eyeglasses in order to shorten the focal point so that the image will appear focused on the retina? Explain.

Sample Conclusion from Experiment 3:

When our lens had air inside, we had no magnification. Water some magnification and mineral oil produced a higher magnification. One conclusion here is that the refraction index of water is higher than air and the refraction index o f mineral oil is higher than that of water.

The other conclusion is that the type of material does affect the focal length. Mineral oil lens had a lower focal length than water lens.

To make sure that the result of our experiment is valid, we searched some books and the Internet for refraction index of water and refraction index of mineral oil. We found that the refraction index of mineral oil is higher than that of water.

Possible Errors:

If you did not observe anything different than what happened with your control, the variable you changed may not affect the system you are investigating. If you did not observe a consistent, reproducible trend in your series of experimental runs there may be experimental errors affecting your results. The first thing to check is how you are making your measurements. Is the measurement method questionable or unreliable? Maybe you are reading a scale incorrectly, or maybe the measuring instrument is working erratically.

If you determine that experimental errors are influencing your results, carefully rethink the design of your experiments. Review each step of the procedure to find sources of potential errors. If possible, have a scientist review the procedure with you. Sometimes the designer of an experiment can miss the obvious.

Reasons for Error:

Petroleum jelly between water lens and slide, possibly causing distortion in the view. Insufficient water seal, water was leaking out of the seal

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