# What is always true about an image as it appears through a diverging or concave lens?

PHY112 On-line Lab # 10 Optics & Lenses

Lab #10 Optics & Lenses

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Introduction:

Optics is the branch of physics that studies the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light.

In this lab we will be exploring some the basic principles of optics, in particular as it relates to interaction with thin optical lenses. There are basically two type of optical lenses, Converging and Diverging . These two types are pictured below and left.

Converging lenses, as depicted to the right, focus parallell light rays to a single point. This point is known as the focal point (F) of the lense. The location of the focal point varies with the shape and the size of the lens. The distance from the center of the lens to the focal point is called the focal length (f) of the lens.

A diverging lens makes parallel light rays diverge or spread out. The focal point of a diverging lens is that point where the diverging rays would converge if they were projected back.

Ray Tracing is a method used in optics to determine the location, size, and orientation of an image as it appears through a lens. When doing a ray tracing diagram, it is customary to draw three lines representing specific light rays. This is illustrated below for a convex or converging lens. Take a moment or two to study the three diagrams so that you understand the basic process.

Part I [Instructional video]

Now, watch the following video and then you can answer the questions below in the spaces provided. https://youtu.be/mfytZxM8lho

1) The narrator of the video uses an analogy to explain how light is refracted when it passes through a medium. What analogy does he use? Does this make sense to you? Why or why not?

2) In your own words, explain how the focal point (f) and 2 times the focal point (2f) are related to the curvature of a convex or converging lens.

3) What is the difference between a Real Image and a Virtual Image ?

4) What kind of image will you get when an object lies outside of the focal point?

5) What kind of image will you get when an object lies inside of the focal point?

6) What is always true about an image as it appears through a diverging or concave lens?

Part II [PhET simulation]

Go to the Geometric Optics PhET simulation at: https://phet.colorado.edu/en/simulation/legacy/geometric-optics

You will see the screen below. Follow the instructions and answer the questions on the next pages.

7) Move the Curvature Radius slide back and forth, how do changes in this value affect the image and the location of the focal point?

8) Refractive index , also called index of refraction , is a way of measuring the amount of bending that a ray of light experiences when passing from one medium into another. Move the Refractive Index slide back and forth, how do changes in this value affect the image and the location of the focal point?

9) Move the Diameter slide back and forth, how do changes in the diameter of the lens affect the image and the location of the focal point? Why do you think that the daimater size has this particular effect on the image?

10) Now, maximize all three slides. Check the Virtual Image box on the control panel. Move the object, slowly towards the focal point. What happens to the image? Is this what you would have expected form watching the video in part one? Why or why not?

Part III [Calculations]

There are some simple basic formulas that are used in lens optics. These formulas are particularly important for Optometrists, Opticians, telescope and microscope manufacturers, along with many other professions. Watch this brief video to get an overview of these equations:

The two equations from the video that we will be most interested in are the following:

1)

Where:

P = power; f= focal length; R = Curvature Radius; di = distance to image; do = distance to object

(note: distances must be measured in meters)

The unit for Power is a Diopter . In optics the two words are often used interchangeably.

2)

Where:

M = Magnification; di = distance to image; do = distance to object; hi = height of image;

ho = height of object

Now go back to the PhET simulation: https://phet.colorado.edu/en/simulation/legacy/geometric-optics

Use the reload page button to reset the variables to their staring values.

11) Check the Ruler box on the control panel.

Use the moveable ruler to measure the distance

between the focal point and the far edge of the lens (be

sure to convert to meters). What value do you get?

Now use equation 1 to calculate the power in diopters.

What value do you get?

12) This PhET simulation has one serious flaw. It has to do with the control panel and the value displayed for Radius of Curvature. Do you see it? In question 11) you just measured the focal length of the lens. By definition, the Radius of Curvature should be twice the focal length. What value should it be displaying at the current focal length?

13) Now measure the distance between the object and the center of the lens. (It is easiest to measure from the tip of the pencil) Next, measure the distance between the image and the center of the lens. Don’t forget to convert to meters. What values did you get for each? Now use Equation 1) to calculate the power again, this time using the two measurements that you just made. What power do you calculate? Does it agree with your answer from question 11 above?

14) Using equation 2) calculate the Magnification. What value do you get?

15) Now, using the ruler, set the distance between the object and the center of the lens to 120 cm. Next measure the distance between the image and the center of the lens.What value do you get?

Next, using Equation 2) calculate the magnification. What value do you get? Looking at the image on the screen, does this seem to be correct?

16) For our final question you need to minimize the Radius of Curvature slide (remember the display is indicating half of the actual value).

You also need to maximize the refractive index.

Now set the object at 100 cm from the center of the lens (you may have to move the ruler around a bit to see exactly where it is because the lens becomes quite opaque at a high refractive index.)

Next measure the distance from the image to the center of the lens.

Record both of your measurements below.

Finally, use Equation 2) to calculate the magnification. What value do you get?. Looking at the image on the screen, does this seem to be correct?

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