Optics Unit Lab Report
- By Evan Chan, Evan Kolm, and Nari Farhangi

Introduction:
Throughout the different optics labs, we explored the interactions between light and magnification lenses and their properties. Through our investigation, we were able to hypothesize about different laws regarding the ways in which light is affected by different kinds of lenses. We also analyzed the difference between a real and a virtual image. Using the Optics Expansion Kit, and the program "Logger Pro," we were able to build our understandings of the behavior and properties of light in general and draw conclusions based off of our numerical results.

onegaishimasu

#1. Light and Distance Lab:
Description and purpose: In this lab, we placed a light source and a Vernier Light Sensor on the track provided by the Optics Expansion kit and used it to measure the intensity of the light and different corresponding distances from the sensor. In order to find the relationship between the distance from the light source and the intensity, we moved the light sensor gradually in small intervals and collected data. After recording our results, we plotted our data on a graph and fit it to a curve. This curve explains the relationship between distance and light illumination in a graphical perspective. By doing this, we were able to derive a mathematical formula that explains this relationship.

Results: 










Conclusion: After several trials, we found that as the distance from the light source increases, the intensity of the light decreases. We derived an equation for the  exponential decrease of the intensity of the light as the distance from the light source increases by plotting points and finding an equation that fit them, which is depicted in the images above.

Wrap Up:

1. How does the power passing through the inner sphere compare to the power reaching the outer sphere?

-The same amount of power passing through the inner sphere and reaching the outer sphere are the same

2. How do the surface areas of the two spheres compare?

-The outer sphere has a larger surface area

3. In general, then, how will the intensity vary with distance from the source?

-As the distance from the light source increases, the intensity of the light will decrease

#2. Thin Lens Lab:
Description and purpose: In this lab, we used convex convex lenses to project real images on a screen. We attempted to track the distances between the lens and the light source (the object distance) and the lens and the screen (the image distance), which would produce the real images. We used these results of different distances in order to determine the relationship between object and image distance. We plotted these results on a graph, and then produced an equation that would describe this relationship. We also plotted the inverses of the image and object distances and eventually discovered that the equation of the inverse graph was the original thin lens equation. This finding provided us with a clear understanding about the relationship between the object distance, the image distance, and the focal length. 

11. Look at the fit for 1/do vs. 1/di. Identify the y-intercept, “b,” in the equation. What is the significance of the value? (Hint: Examine the inverse, or 1 over the Y-intercept. What are the units of the Y-intercept?)

b=.1011 1/di=-1.038/do+.1011 → 1/di+1/do=1/10=1/(10cmconvexlens)

1. Using the graph of the inverses for the 10 cm double convex lens, predict where you would be able to find an image if you placed the light source 33 cm from the lens. 1/10=1/33+1/x → 33/330-10/330=1/x 1/x=23/330 x=330/23

2. Using the thin lens equation, predict the image distance for a lens with a 20 cm focal length when an object is placed at 33 cm. 1/20=1/33+1/x → x/20-x/33=1 33x-20x=(20)(33)=660 → 13x=660 → x=660/13

3. Predict the y-intercept of the 1/do vs. 1/di graph if you were to repeat the experiment with a lens with a 15 cm focal length. =1/15

4. Where would you place the screen if the light source were positioned 33 cm from the lens with a 15 cm focal length? 1/15=1/33+1/x 33x-15x=(33)(15)=495 → 18x=495 → 2x=55 → x=55/2

Extensions:

1) The ratio between the image distance and the object distance should be equal to the magnification, or the ratio between the heights of the image and the object. Add a calculated column to your table with the magnification for each configuration. Under what conditions is the magnification the greatest? 

- The magnification is the greatest when the image distance is greater than the object distance. 

Wrap Up Questions:

1. How do you think a lens makes an image?

- A lens creates an image by refracting (converging or diverging) light rays that pass through it. All these rays of light meet or converge in the focal point.

2. What factors might determine the size of an image?

-The factors that determine the size of an image are the thickness of the lens and the distance of the light source from the lens.

3. What factors might determine whether an image is clear and in sharp focus?

-The factors that might determine whether an image is clear are the lens (focal length, aperture and distance from the image center) the movement (or lack of) of the lens, and the distance the image is from the lens.

4. What is special about the location where the lens projects a clear image for an object very far away? Is this location the same for other lenses?

 - The type and size of a lens changes the location where the projection is a clear image. In this case, the 
lens that projects a clear image from a far away distance is physically smaller than the length of the focal length. These lenses are long focusing and extend the path of light on the object. This location is distinct for other lenses because it is where all the rays of light converge and is blurry without these special circumstances.

#3. Build A Telescope:

Description & Purpose: In this lab, we investigated virtual and real images using lenses and a refracting optical telescope. With the use of the Dynamics Systems track and optics kit, we were able to build a telescope using two convex lenses and a screen. We then pointed it towards a window, which provided for a light source that projected an image onto the screen (between the two lenses). After focusing the image by moving the screen, we realized that the projected image was inverted and upside down because of the converging lenses. We then further experimented by switching out different lens magnifications (ranging from 10-20 mm); this allowed for us to determine the correlation between the lenses.

Conclusion: “In a refracting optical telescope, a real image of a distant object is produced in the space between the lenses. A second lens produces a magnified virtual image” -- we came to the conclusion that when a larger lens is placed directly at the front of the telescope, and a smaller lens is placed in the back (towards the eye), the projected image appears to be larger. When a smaller lens is placed in the front, and a larger in the back, the image appears to be smaller; and when both lens sizes are identical, the projected image appears to maintain the same size and proportions -- with the telescope, we were able to determine the effects of different converging lenses on the original, real image produced by the window light, and the virtual image seen by the eye through the second lens.

Extension

The Galilean telescope.

http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/teles.html

#4. Aperture and Depth of Field  

Description and Purpose: In this lab, we investigated the role of apertures in image formation. We first set up an LED light source, a convex lens with an aperture attached, and a screen on the systems track -- to predict and observe the effect of aperture adjustments on real image formation, we filtered through the different openings of the aperture to focus their individual effects on image production via light reduction. We then moved onto the second part of the lab, where we observed the relationship between aperture and depth of field: this time, we left the aperture(s) untouched, and moved the projection screen instead. This allowed for us to investigate the direct correlation between the amount of light being projected, and the clarity of the real image. Conclusion: We came to the conclusion that the size of the aperture does affect the clarity and strength of the projected real image but, no matter the shape, the image will always retain its proportions and dimensions (i.e. the D-shaped hole did not affect the shape of the light’s projection on the screen). The smaller the aperture holes were, the brighter and sharper the real image was, because of the amount of light being let through. As an observation between aperture and depth of field, we concluded that the smallest holes had the largest depths of fields, whereas the larger holes were lacking in this quality. Overall, this lab came to prove all of our predictions wrong -- the smaller the aperture, the more powerful the real image turned out to be.

4. Place the aperture assembly on the track, immediately adjacent to the lens at around 30 cm. (Either side is OK.) Describe the image you see on the screen.

- same size, slightly dimmer

5. The aperture has a setting that covers half the lens vertically, so the opening is in the shape of a “D.” Predict how the appearance of the image will change when half the lens is covered.

- dimmer and to the side of the D

6. Adjust the aperture assembly to the D-shaped opening. What do you observe? How does that compare with your prediction?

- dimmer but in the same position

7. Predict what will happen to the image as the round aperture is made smaller and smaller. Try it. What do you observe? How does that compare to your prediction? Why might this be happening?

- dimmer and dimmer etc. because less light is getting through

Using the same setup as in Part A, turn the aperture to one of the mid-sized openings. Move the screen toward and away from the screen. When is the image in focus? Is the image only in focus at a fixed location, or is there a range over which the image appears to be in focus? Over what distance can you move the screen while keeping the image in focus?  Note: Being “in focus” is sometimes tricky to evaluate when the image is changing size; use your best judgment.

- you can move .75 cm in either direction and still stay in focus

2. Predict: Look at the different openings on the aperture apparatus in your setup. Do you think the larger or smaller apertures will produce greater depths of field? Justify your answer.

-The larger aperture will have a greater depth of field because more light is being let through.

4. Set the aperture to the largest setting. Beginning with the screen far away from the lens, move the screen closer until the image produced first appears to be in good focus. Record the distance.

-Distance with the biggest hole: 49.8 from screen to light source.

5. Continue moving the screen toward the lens until the image just begins to lose focus. Record this second distance.

-Distance with the biggest hole: 49.1 cm from screen to light source.

6. Find the difference between the two distances to calculate the range of focus. Record this value in the Data Table.

-Range of focus: 0.7cm

7. Repeat Steps 4 - 6 with each of the round apertures, with 5 being the largest, and 1 being the smallest. Which aperture has the greatest depth of field?

As the aperture gets smaller, the range of focus increases

Extensions

1. Research the term “f-stop” in photography. How do the f-stop values relate to the values for aperture in your table? What tradeoffs are involved in the decisions a photographer makes with respect to f-stop?

-In photography, the “f-stop” represents the ratio of the lens’ focal length to the diameter of the optical image of the aperture stop.

2. Research the cause for the improved depth of field which results from a small aperture.

-An aperture, which determines how much light will travel through the lens and fall on the image sensor, is measured in “f stops.” The aperture and its f stop have an inverse relationship, such that a smaller f stop corresponds to a larger aperture. This larger aperture would result in a smaller depth of field. Therefore, a smaller aperture would have a larger f stop, and as a result, a wider depth of field.

Dedicated to baby Friedman

Sensei,
Thank you very much!