course phy202
With the thicker convex lens, when the light is 50cm from the screen, the screen must be moved to 6.8cm to make the sharpest image (h<1mm). When the light is 40cm from the screen, the screen must be moved to 7.1cm to make the sharpest image (h=1mm). When the light is 30cm from the screen, the screen must be moved to 7.5cm to make the sharpest image (h=1.25mm). When the light is 20cm from the screen, the screen must be moved to 8.6cm to make the sharpest image (h=2mm). Next, I positioned both lights 3.5cm apart and 50cm from the lens, obtaining the sharpest image with the screen 6.8 away from the lens and the images <1mm apart (h<1mm). Because the rays of light passing through the lens are refracted toward the center of the lens and because the two light sources are positioned off center to either side of the lens, the images on the screen appear on the opposite sides of their respective light sources. So, covering up the left light source makes the right image disappear. Next, I positioned both lights 3.5cm apart and 30cm from the lens, obtaining the sharpest image with the screen 7.5cm away from the lens and the images roughly 1mm apart (h=1.25mm). Next, I positioned both lights 3.5cm apart and 20cm from the lens, obtaining the sharpest image with the screen 8.6cm away from the lens and the images roughly 2mm apart (h about 2mm). Next, I positioned both lights 3.5cm apart and 9cm from the lens, obtaining the sharpest image with the screen 18cm away from the lens and the images 7cm apart (h=1cm). Next, I positioned both lights 3.5cm apart and 7cm from the lens, obtaining the sharpest image with the screen 42cm away from the lens and the images 21cm apart (h=3cm).
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Next, for the spotlight part of the experiment, I kept the light 6cm away from the lens and began moving back from the wall. The image on the wall appeared to be the same size and shape of the actual lens when the lens was also 6cm away from the wall. The farther away I moved from the wall with the light 6cm away from the lens, the larger and blurrier the image on the wall became. Regardless of my distance from the wall, the image was never as clear as when I kept the light exactly 6cm from the lens.
Next, for the image creation part of the experiment, I used the paper my lens came wrapped in and I folded it up into a 'V' shape. I used the thicker convex lens as the image forming lens (IFL) and I used the thinner convex lens as the spotlight forming lens. I found more variability in these trials than before because I had to focus the light through second lens to form a spotlight on the object this time, instead of the light simply being the object. Nevertheless, my findings were roughly similar. When the object was 40cm from the IFL, the sharpest image formed with the screen about 7cm away. When the object was 30cm from the IFL, the sharpest image formed with the screen about 7.5cm away.
Next, I will use the thin lens equation (1/f=1/o+1/i) for the 1 light trials: o=50cm,i=6.818cm. o=40cm,i=7.059cm. o=30cm,i=7.5cm. o=20,i=8.571. These same calculations also apply for the same distances used in the 2 light trials that followed, including o=9cm,i=18cm and o=7cm,i=42cm
Next, for the spotlight experiment, at first I was confused trying to apply the thin lens equation because the ""image"" on the wall got larger as I backed away. Then, I realized what was different this time: I was holding the light source at the focal length of the lens, which resulted in an ""infinitely"" long image distance. So, I wasn't actually seeing an image of the lens on the wall during this trial. Rather, I was seeing the spotlight I created by dispersing the light through the lens at a distance too close to produce a visible image of the lens as predicted by the thin lens equation.
Next, for the image creation trials, the thin lens equation confirms the 40cm and 30cm trials just like in the preceding trials. It just took longer to determine this because I had to play with the second lens for awhile to create the appropriate sized spotlight to resolve the image on the screen through the IFL.
Next, for the image heights, I confirm with the equation magnification=hi/ho=-(di/do). For do=50cm,di=6.8cm,ho=.5cm,hi=.07cm. For do=40cm,di=7.1cm,ho=.5cm,hi=.09cm. For do=30cm,di=7.5cm,ho=.5cm,hi=.125cm. For do=20cm,di=8.6cm,ho=.5cm,hi=.21cm. For do=9cm,di=18cm,ho=.5cm,hi=1cm. For do=7cm,di=42cm,ho=.5cm,hi=3cm.
Next, I confirm that the inter-image distances are to the inter-object distances as the image distances are to the object distances from the lens: 6.8:50=.476:3.5. 7.5:30=.875:3.5. 8.6:20=1.5:3.5. 18:9=7:3.5. 42:7=21:3.5.
I see evidence that the two light sources are inverted when I cover up the left lens and observe the right image disappear, as I described above."
Excellent work.