Physics II Lab 13

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Feb 20, 2024

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Name: Chloe McGonagle Date: 10/8/23 Instructor: Part 1 of the lab is modified from the ‘Optics Simulation Lab’ contributed by Edward Redish from the University of Maryland, College Park. Introduction: All of our analysis of the physics of vision — lenses, mirrors, and images — follow from the careful application of a few basic principles: The general physics:  Certain objects (the sun, bulbs, etc) give off or emit light.  Through empty space (or air) light travels in straight lines .  Each point on a normal object scatters light, spraying it off in all directions. The physics of a thin lens (based on a few simplified rays):  Rays that pass through the center of the lens go straight through.  Rays coming at the lens perpendicular to plane of the lens, or parallel to the principal axis (the line perpendicular to the lens surface and through the center of curvature of the lens) are bent so they go through a single point on the far side of the lens known as the focal point . The focal point is a fixed distance from the lens (called the focal length ) that depends on the curvature of the lens surface.  A thin lens has focal points on both sides of the lens, each at the same distance from the lens. The simplified physiology:  We only see something when an object’s light rays enter our eyes.  Our eyes identify a point as being “on an object” when rays traced back converge at that point. If there is no actual object at that point, we call the convergence point an image of the original source.  Your brain constructs your visual field using the assumptions that (1) light travels in straight lines and (2) sources are found where the rays trace back to, so it looks to us as if the source is at the position of the image.

The Simulation We will explore the way light behaves and the rules described above using mirrors and thin lenses by using a ray optics simulation at https://ricktu288.github.io/ray-optics/simulator/ This program lets you do a lot, but it is fairly complex to use. Spend several minutes exploring what you need to do to create, delete, and move around objects.  The sources — a single light ray, a beam of rays, a point source of light  The measuring tool — a ruler  The device —a thin lens (Glasses → Ideal lens).  The views — Rays, Extended Rays, All Images, and Seen by Observer o At first only use the Rays view. After you have created images with a mirror or a lens, explore the other views and figure out what they do.  Hint: Once you have placed objects and rays, to get the program to stop controlling them and let you just scoot the constructed objects around, choose "Move view". You can then move the object and source you placed, or the entire view. Lens with point sources Reset your screen by choosing "Reset" from the File menu. 1. Place a vertical thin lens in the middle of your screen by choosing "Glasses → Ideal lens" from the Tools menu. Select “Ray” from the tools menu to add a light ray on the left side of the lens.

Arrange the ray so that it goes through the lens at an angle. Your screen should look like the figure at the right. Note that the ray has two red dots on it. If you move either of the red dots, this will change the angle of the ray. If you grab the ray between the red dots, this will move the ray parallel to itself. Explore what happens as you move the ray in various ways. Include a screenshot below with the simulator and include your name and date. 2. Make sure the view is set on "Rays". Delete your original ray by right-clicking (Windows) or Shift-clicking on the ray (Mac). Add a point source to the left of the lens. The point to the right

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of the lens where the rays meet is called a real image . Describe what you see as you move the source towards the lens and away from the lens. On the left, the point source kind of looks like a yellow star with yellow beams coming out of it at all directions uniformly. The beams are coming out at angles around the point source; however, when the beam hits the lens, a mirror version of the beam comes out of the other side of the lens. Originally the beams that are more at an upward angle when hitting the lens are now downward and vice vera. Additionally, with the beams that have hit the lens, they also form a smaller version of a point source where all the beams come together and meet. Then once they meet, they all go out again in the reverse direction from the lens. 3. At some distance from the lens you should not have found an image. Turn on the “Extended Rays” option in the view menu. You should now see that at those distances, while the refracted rays do not meet anywhere, the extended rays do. The point where the extension of these rays meet is called a virtual image . Is it on the left or right side of the lens? Include a screenshot or image of the virtual image.

The virtual image is formed behind the same side of the object from the lens. Since the light extension rays travel from right to left through a lens, the virtual image is formed on the right side of the lens. Lens with an incoming beam of parallel rays. We'll now explore another feature of the lens by using a beam of parallel rays rather than a point source. 4. Remove your point source and instead create a parallel beam by choosing "Beam" from the Tool menu and arranging the beam source (green line) so that it is parallel to your lens and aimed right at its center. Your screen should look like the figure at the right. You'll see that the lens brings all the parallel rays together at a single point. This is called the focal point or focus of the lens, and the distance from the focal point to the lens is called the focal length . Measure the focal length using the “Ruler” from the Tools menu and report your result. Focal length= 140cm

5. Now turn the ruler vertical and put it at the focal point. Your screen should look like the figure at the right. Now move the beam up and down and left and right. Describe what happens to the focal point. As the beam goes up, the focal point after the ruler goes the inverse direction, meaning it goes down. Additionally, when the beam goes down, the focal point after the ruler goes up. The part that is before the focal point but after the lens goes the same way as the start of the beam. Thin Lens Equation and Magnification.

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6. For this next part we want to measure the position and the size of the object and image, so we need to have a more carefully created setup. Delete all your objects and start again (Reset).  Create a new lens. You can assure that it is vertical by holding the shift key while you draw it.  Draw a ruler starting from the center of the lens and pulling out to the right while holding the shift key to make it horizontal (for measuring the image distance).  Draw a similar ruler to the left by starting at the center and pulling to the left (for measuring the object distance). Your screen should look like the figure below. (You may have to draw the rulers somewhere else and then move them into place.) This is considered your principal axis. Now place a vertical ruler at some distance on the left, beyond the focal point, going up. We will be using this location for the object distance. Put a point source somewhere along the ruler and so that there is an image. Determine the image distance, and put a ruler at that location, but going down. Switch to "All Images" view, and you should see something like what is shown below. Don’t worry if your object and image distances are different from what is shown here.

Select “Ruler” from the tools menu and draw a ruler through the center of the lens. Keeping the source on the principal axis, place the source at four different distances and collect data on -distance of the source from the lens (object distance, d o ) and -distance of the corresponding real image from the lens (image distance, d i ). A data table is included at the end of this section. The focal length can be found from: 1/(object distance) + 1/(image distance) = 1/(focal length) -The distance from the principal axis to the object is (green dot below) the object height (h 0 ) -the distance from the axis to the image (yellow dot) is the image height ( h i ) as shown in the figure below, where the object (on the left) and the image (on the right) are represented by arrows. Note that the image height will be negative in this case. The magnification ( m ) can be found by m = -d i /d o or h i /h o . Complete the table below for your four scenarios. Include a screenshot of one of the four scenarios (different object distances). Object distance (cm) -distance from lens Image distance (cm) Focal Length (cm) Object Height (cm) Image Height (cm) Magnification

1 OD:-400cm ID: 150cm FL: -1/(400) + 1(150) = 1/FL =.0025+.0067 =.0042 =1/.00917 FL= 238.095 cm OH: 130cm IMH: -50cm Mag: m=-di/do or hi/ho -50/130 Mag= -0.384 2 OD: -210cm ID: 190cm FL: 1(-210) + 1(190) =1/FL -0.00476 + 0.0052 =0.00050316 FL: 1,987.44 cm OH: 40cm IMH: -30cm Mag: -0.75 -30/40

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3 OD: -300cm ID: 150cm FL: 1(-300) + 1(150) = 1/FL -0.0033+ 0.0067 1/.003367 FL:297cm OH:150cm IMH: -70cm Mag: -0.467 4 OD: -250cm ID: 170cm FL: 1(-250) + 1(170) = 1/FL -0.004 + 0.0058 =1/0.00188 FL: 531.91cm OH:20cm IMH: -10 Mag: -0.5

7. Repeat this exercise for a lens with a negative focal length (there is a slider when you draw the lens). Any image distance to the right of the lens will be positive, while any image to the left of the lens will be negative. Include a screenshot of one of the four scenarios. Object distance (cm) Image distance (cm) Focal Length (cm) Object Height (cm) Image Height (cm) Magnification 1 OD: -50cm ID: -100cm FL: 1(-50) + 1(-100) = 1/FL -0.02 -0.01 = 1/FL 1/-0.03

FL: -33.33 OH:10cm IMH:20cm Mag: 2 2 OD: -50cm ID:-100cm FL: 1/(-50) + 1/-100) = 1/FL -0.02-0.01 1/0.03 FL: -33.33cm OH: 50cm IMH: 110cm Mag: 2.2 3 OD: -30 cm ID: -50cm FL: 1(-30) + 1(-50) = 1/FL -0.033 – 0.02 1/-0.053 FL: -18.87 OH: 30cm IMH: 40cm

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Mag: 1.33 4 OD: -50cm ID: -100cm FL: 1/-50 + 1/-100 = 1/FL -0.02-0.01 FL: -33cm OH: 120cm IMH: 240cm Mag: 2

Part 2. Lens Exploration You should have six lenses and a mirror with your lab kit. For each of these trials, pick an object that is several meters away, like a picture or object across a room. You will view the object through each of the lenses provided and describe the behavior. 1. Take the Double Convex Lens. What is the listed focal length on the package? 150mm. In your hand, hold the lens out as far as possible, and try to focus on the object across the room that you’ve selected. Is the object inverted or upright? Smaller or larger? Can you focus the object, or are you unable to? Slowly move the lens towards your dominant eye (or towards your eyeglasses). Describe what happens to the image as it gets close to your eye. The object is inverted. I am able to focus it when I move it slowly and hold it over around where the top of the object is. The object appears a bit smaller. As the lens gets closer to my eye, the object becomes alrger and it is unable to focus. 2. Take the Double Concave Lens. What is the listed focal length on the package? 150mm. In your hand, hold the lens out as far as possible, and try to focus on the object across the room that you’ve selected. Is the object inverted or upright? Smaller or larger? Can you focus the object, or are you unable to? Slowly move the lens towards your dominant eye (or towards your eyeglasses). Describe what happens to the image as it gets close to your eye. ‘ The object appears upright. It is also smaller than what the double convex lens showed. It is very clear and easy to focus. As I move the lens towards my eye, it gets a bit larger and never goes out of focus. 3. Take the Plano Concave Lens and the Plano Convex Lens and do a similar procedure as in the previous two parts. You do not need to record individual results. Place the lenses together and repeat. What do you observe? Concave- similar to double concave (smaller image, easy to focus, stays focused as moves closer towards eye) Concave- upside down and very hard to focus, image appears larger Together- object appears as it is, larger and upright. Stays focused as lens comes closer to eye. Does not get bigger or larger when comes closer, can just see right through

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4. Take the two combination convex/concave lenses of different focal lengths, and look at the item across the room. Describe similarities and differences between the images formed by the two lenses. Similar: both upright images DC: object appears blurry and is zoomed in, hard to focus PC: Very clear and object not zoomed in, easy to focus 5. Out of all of the lenses present, which lens do you think works best as a magnifying glass and why (there may be more than one correct answer given the materials and object distance chosen). I think the PC convex magnifies the object the most. Out of all the lenses, the PC convex magnified the object the most from across the room. Convex lenses are thicker in the middle and thinner on the outside meaning when light passes through the lens, it refracts the light and then brings it together at the focal point. At the focal point is where the lens is able to magnify the object. Convex lenses cause light rays to converge which causes magnification. 6. Take the double-sided mirror. Starting with the convex side, hold the mirror out as far as possible, and try to focus on your reflection. Is the object inverted or upright? Smaller or larger? Can you focus on yourself, or are you unable to? Slowly move the mirror towards your dominant eye (or towards your eyeglasses). Describe what happens to the image as it gets close to your eye. With the convex side, my reflection looks smaller and further away than it normally would. My reflection is the right side up and I am able to see a broader viewpoint than I normally would. As I move the mirror further, the convex side of the mirror appears to still be getting smaller. 7. Take the double-sided mirror. With the concave side facing you, hold the mirror out as far as possible, and try to focus on your reflection or an object behind you. Is the object inverted or upright? Smaller or larger? Can you focus on yourself or the object, or are you unable to? Slowly move the mirror towards your dominant eye (or towards your eyeglasses). Describe what happens to the image as it gets close to your eye. With the concave side, my reflection is inverted. My reflection is also enlarged/ larger than the convex side. As I move the concave side further to me, it continues to enlarge my image.

8. Based on your observations, which mirror side (convex or concave) would work for seeing object around a corner? Convex mirrors are better to see around corners. Convex mirrors allow images to be virtual and upright but also smaller than the actual scene. You are able to see more of the road than you otherwise wouldn’t be able to.

Physics II Lab 13

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