Journal

Wednesday 7.20.2011

I was looking up cavity stability today and found out that it depends on the radii of curvature of the two mirrors and the distance between the two mirrors. I found that with a cavity with one plane mirror and one concave mirror, the cavity is stable when the two mirrors are placed between 0 and R, the radius of curvature of the concave mirror, apart. I think that the most stable distance would be between these two distances at the focal length of the concave mirror. The focal length of the mirror that I have is 2.5 cm and a cavity if this length would exactly fit over the cuvette mount.

Laser Sam came in today to give us an introductory talk on lasers and laser safety. He will be staying with us until Friday afternoon and hopefully he will be able to help me a lot in figuring out how to increase the power and efficiency of my laser.

I am also still taking measurements of the ND slide. Dr. Noe told me to use the HeNe laser because it will give me clearer results. However, because the HeNe laser gives out 30 mW of power, I had to attenuate it with another ND filter in front of the photodetector. After taking the readings I analyzed the numbers that I got and found that the loss in the slides increases as I go into the darker regions of the slide. I'm going to retake my data to see if I get similar results again because the loss does seem very high for the slide.

Tuesday 7.19.2011

Today I continued trying to make reflectivity measurements for the neutral density filter. However, the numbers that I got for reflectivity were very large. I think that perhaps the photodetector was detecting alot of the light from the flourescence of the cuvette and not necessarily just the reflected laser light. The reflectance continually increased as the filter got darker until I got to the very darkest section when the reading on the photdetector dropped. I'm not quite sure what is going on and how to fix my setup to avoid these things.

I have also been going through different calculations for which concentrations I should take measurements for. I originally wanted to use rhodamine but I didn't realize that there was such little rhodamine left so I decided to just keep using the Coumarin 500. I decided to double the recomended concentration and make a 25mg/20ml solution. Add two ml of that into the cuvette and then make readings of the power as I add 1ml at a time into the cuvette solution until I have 10 ml of solution. This brings me from a 9.72E-3 molar concentration down to a 1.94E-3 molar concentration. I didn't have anything to measure the exact volume of the cuvette but it seems to be around 10 ml. I have measured out exactly 25 ml of Coumarin but I don't yet have anything to precicely measure the methanol.

Monday 7.18.2011

Last week, Dr. Cohen and Dr. Noe suggested that I use a particular neutral density filter to come out with some measurements of reflectivity and cavity gain. This filter has a number of bands of gradually increasing optical density. First I did some tests on the transmittance of the different bands and found that the lighest band had a 96% transmittance and the darkest band had a 40% transmittance. I then tried to do some tests on the gain by making sure that the beam was being reflected back into the cuvette and measuring the output power through the ND slide. However, the data that I got for that setup read that the power decreased as the transmission decreased. So I decided to so some reflectance readings on the filter to see whether all of light that wasn't being transmitted was being reflected back. However, as I was trying to do the measurements, things kept going wrong and the measurements kept being interupted. I'm going to have to do these readings over again tomorrow.

Dr. Noe and Dr. Cohen are also talking about getting a concave mirror to use as the high reflective mirror so I did some reasearch on how to set up a cavity with one concave mirror and one planar mirror. This kind of cavity is considered a stable cavity because even if the light ray is slightly off axis, this cavity will keep sending it back through the gain medium. The plane mirror also has to be at the focal point of the concave mirror in order for this kind of cavity to work wich means that I want to have a mirror with a focal length between 3 and 5 inches.

As of now I have three major things that I have to work on. I have to get data on how the reflectivty of the output coupler effects of the gain, how the dye concentration effects the gain and the how the concave mirror will effect the characteristics of the laser beam.

Wednesday 7.13.2011

Today, I kept fiddling with the laser and got more familiar with how to line everything up and get the brightest spot that I can. So I got the lasing through the cuvette and then had a reasonable amount of light coming through the output coupler. Then, when I tilted the cuvette on the stand, I found that there was still lasing through just mirrors which means that I had the mirrors lined up well enough to induce lasing. I knew that the cuvette wasn't lasing because when I blocked one of the mirrors, the laser spot went away.

We also had our LTC lunch meeting today. Professor Metcalf suggested that I talk to Andre about getting a transmittance mirror and he also talked about the possibility of getting a slide that had a graduating reflectivity. He also suggested that when I make my next solution, I make a very concentrated solution then keep diluting the solution until I figure out what an optimum concentration is.

Tuesday 7.12.2011

We have lasing! Dr. Noe was still sick today but it was a very good day. Professor Metcalf came in today to help us out and answer any questions that we had. I asked him what my options were to increase the power of the nitrogen pump laser and his response was to take the laser apart and see what we could do with it. The result was that we found that the front plate of the laser was actually an attenuator and not actually part of the laser. The plate was actually blocking a lot of the laser light and you could even see on the inside of the plate where the UV light corroded the plate a little bit.

So as soon as we took that plate off, there was a ton more light getting through and a lot more power was getting to the dye cell. The beam of light also spreads across the length of the cell now whereas before it was just covering the middle section. Luckily, I had the dye cell lined up vertically enough to have it start lasing through the cuvette walls as soon as the front plating was removed!

I want it to start lasing through the cavity and not just in the cuvette so I used the lasing from the cuvette to line up the cavity mirrors. So far, when I tilt the cuvette so that it no longer lases through the walls of the cuvette, the spot of laser light disappeared.

Then Dr. Cohen came in and suggested that I might dilute the dye solution because it seems that the fluorescence is too close to the cell wall and the light is getting interference patterns from passing too close to the cell wall which makes it hard line up. So I made a two part dilution and the fluorescence did go further into the cell and it made less of a diffraction pattern which made it easier to line up.

Thursday 7.7.2011 Friday 7.8.2011

Thursday I spent the day looking up how I might improve the gain of my laser. I increased the concentration of the dye but that didn't do very much for me. I can't quite think of what I might do other than keep playing with the dye concentration. the laser cavity might not be in line but I doubt that the nitrogen pump laser is giving the dye enough of a population inversion to create lasing at this point. I'm not quite sure how to proceed from here.

On Friday, the REU group went to the Museum of Natural History. We all got to go look at the special exhibits and attended the REU seminar that they hold at the museum. It was interesting to see how the program there ran their seminars. All of the students there have to do a couple of presentations in order to work on their presentation skills. The students are allowed to pick their own presentation topics and they had a very interesting a broad range of topics. It was hard to follow because I don't know very much about neither geology nor astronomy but they were interesting none the less.

Wednesday 7.6.2011

I tried to set up my cavity today but its very hard because I have two plane mirrors which are very hard to set up. Dr. Cohen suggested that I line the mirrors up with a different laser so I set up a HeNe laser and lined up the mirrors so that the laser light was going directly back from where it came. This part worked our reasnably well but I put the dye cell back in but there was still nothing coming out.

Dr. Cohen and Dr. Noe think that it would be best to try and use mirrors from a HeNe laser and try to use those mirrors which will be concave and much easier to line up than two plane mirrors. In order to do this, we are going to have to actually cut the cavity of the laser that we decide to use and I'll end up with two pieces of mirror that are probably going to stil have a little bit of glass on the ends of them. These mirrors will not let me make a tunable laser but if I get it to work, it will hopefully set me on the right track to making the laser tunable.

Tuesday 7.5.2011

This is a short week because we had Monday off and today was our REU lecture. Professor Metcalf talked about BEC and gave us a very understandable introduction to the ideas behind laser cooling and trapping.

I also made my die concentration today. I went to the Van de Graff lab to use the scale that they had there. I was trying to make a 25mg/20ml concentration of the coumarin 500 so I needed a pretty sensitive scale to get it accurate on that level. Luckily they had a very sensitive scale that they let me use in the lab. I ended up with a solution that I was happy with. The next part is getting the rest of the cavity set up to see if anything comes of all of this.

Friday 7.1.2011

Today I collected all of the information I need to actually start mixing the dye. I learned about molar concentrations and calculated the amounts that I would need to reach the molar concentrations of each dye. I decided that I should start with the coumarin 500 because I have a lot of that and I want to experiment with the coumarin first before I to go the rhodamine. The only thing about this thought process is that I might not get enough gain through the coumarin to get lasing.

Thursday 6.30.2011

I managed to get a decent amount of work done today. I moved my station over to a different board that Dr. Noe said that I should use and stacked the nitrogen laser on a pile of text books to make it the right height. I started to set up the laser configuration and got a testube clamp to hold the dye cell.

After that, I tested the loss in the optical elements again. At first, I was just shining the laser beam right onto the photodetector which was connected to a voltmeter with high resistance to integrate the pulse powers but Dr. Noe correctly pointed out that the photodetector was being saturated by the beam and that I needed to attenuate the light somehow. So I put a neutral density filter in front of the beam and discovered that the 150 mm and 200 mm cylinder lenses and the quartz cuvette had around an 8.5% loss while the 100 mm lens had a 15% loss and the plastic cuvette had a 12.7% loss. From this I think that I can say that the 150 and 200 mm lenses are quartz and the 100 mm lens is not. Dr. Noe said that I should also see what number I get if I shine the light through the bottom of the cuvette so that it's only hitting one wall.

I also dug around in the back for something that I could possibly use as an output coupler. I was plesantly surprised to find a couple of partially reflecting mirrors in a drawer labelled 1st surface mirrors. When I shined the green laser at it, I could see the laser beam coming out of the other side. Tomrrow, I'm going to have to test the reflectivity of the mirror.

Wednesday 6.29.2011

Today was our LTC lunch and we all had discussions about where our projects were going and what we have done so far. I talked about my recent developments in the power measurements of the nitrogen laser. We also talked about how I could get the gain of the dye up. The only thing that I could hope to do at this point is try output couplers of different reflectivity.

Tuesday 6.28.2011

I've been reading up on gain and laser thresholds in various text books and also online. The basics of what I've been able to gather so far are that a higher mirror reflectivity, a longer cavity ( Which is why lasers tend to either be very long or have bow-tie cavities ), and a low loss coefficient will help me reach the lasing threshold.

One discouraging thing that I've read on Sam's laser website is that with a 95% reflective output coupler and a 0.96 gain coefficient dye ( Rhodamine 590 ), you would need at least a 5 kW peak pump power to reach lasing which is more that I have.

I've also asked Dr. Noe about what I could use for the output coupler and he has suggested that I could either test to see if the output coupler from a HeNe laser would be useful. This might not work very well because many of these mirrors are constructed so that it only reflects the desired wavelength well while the reflectivity drops off as you get further away from that wavelenght. Another option is that I could get permission to use another lab's vaporizer and coat a piece of glass to my desired reflectivity.

Monday 6.27.2011

Today, I went to Professor Metcalf's lab to look at laser dyes and quartz lenses. We found some very nice laser dyes in a cabinet drawer: there was a litte bit of rhodamine 6G, rhodamine 640, and coumarin. Professor Metacalf also found a cuvette ( Which I will have to clean out because it is caked in some unknown dye) cylinder lens that he thinks could be quartz.

So I went about testing the absoption of the cylinder lens using a photodetector connected to an ampmeter. However, I wasn't getting any readings from that but then Dr. Cohen came in and explained that because the spectral responsivity at that wavelenght is so low that I am probably not going to get a high enough current to read through the ampmeter. Therfore, we connected to the voltmeter and also added a 100 kilo-ohm resistor to increase the voltage that we saw. I then got readings for the cylinder lenses and found that both the the one that I got from Professor Metcalf and the one that I got from our lab had around a 10% absorption.

Dr. Cohen also arranged for us to borrow power meter with an energy detector from another lab. The energy detector was basically a thermal detector and it was very sensitive to any of our body heat so we had to be careful about moving while we were taking the measurement. Unfortunately, we found out that the laser was very weak with an average power on the order of 0.1 mW which comes out to a peak power of 1 kW.

The original specs for the laser said that the peak power of the laser was 30 kW. So the actual power of the nitrogen laser is much lower than I would have hoped for. Now, I have to crunch some numbers to see what conditions I have to meet in order to reach the lasing threshold with the lower pump power that I have.

Friday 6.24.2011

David spent today trying to get the optical fiber to work while the rest of us looked on. He got the laser through the multimode fiber with 70% efficiency. But it got really difficult when we switched to the single mode fiber. We had to turn the lights off just to see the light coming out of the other end of the fiber. The method for coupling the fiber seems tedious but necessary.

Wednesday 6.22.2011

I spent all morning trying to get the power meter to work. At first it just wouldn't work at all so I switched over to a HeNe laser to see if it would read there. Dr. Cohen and I even walked over to the lab that we borrowed the meter in case they could give us any advice on how to make it work. Eventually, I just kept jiggling the wires and it started to work and measured a good value for the HeNe laser. But then when I tried to move it over to the pulsed nitrogen laser the meter just wouldn't read quite right. Dr. Cohen suggested that I call the company and ask them whether the detector would work with the pulsed laser and they told me no, the low power detector probably wouldn't work because it is meant to be used with a continuous wave laser and I would have better luck with a pulsed energy detector.

So now I have no power meter to get a power measurment on the nitrogen laser. Dr. Cohen said that my alternatives would be to calculate the power by measuring the current that is generated in a photodetector. I also have to head over to Professor Metcalf's lab tomorrow to try and get my hands on some dyes and quartz leses.

Tuesday 6.21.2011

We had our REU lunch today. Professor Graff showed us a couple of projects that past REU students did. We looked at a fishtank with a varying index of refraction that caused a laser beam to bend through it. We also saw some experiments on thermal expansion and contraction as well as experiments that dealt with centripetal forces. It was interesting and helpful to see how the students designed their projects with the materials that were available.

I also worked on getting the power meter set up. There is a lot more to working the power meter than I had originally thought and I want to make sure that I use it correctly.

Monday 6.20.2011

In the morning, we had a group discussion. We went over interference and derived the formula for double slit interference. In order to do this, we had to use a binomal expansion which only is true if the distance to the screen is much larger than the distance between the slits.

Then in the afternoon, I spoke to Dr. Noe and Dr. Cohen. We figured that a crucial part of understanding how to construct the dye laser would be figuring out the power/energy output of the pulsed nitrogen laser that we have. I found the original specs for that laser, but those numbers are just a starting point, I still have to test what the specs currently are.

The first step I took in doing that was measuring the pulse width/duration using a photodetector connected to an oscilloscope. Lauren and David helped me with the set up. We first had to clear a space on the work bench and once we did that, we moved the laser over to the other table so we could align everything properly. Once we had everything properly aligned, we started firing the laser. After fishing around on the oscilloscope settings for a while we found a pulse but it looked much larger than the specs said that it should. We originally saw pulses that were a couple of tenths of a microsecond while the specs for a pulse was 4 nanoseconds.

After playing with the laser alignment, we eventually figured out that the laser was saturating the photodetector so that when we moved the laser a little bit out of alignment so that only part of the beam was hitting the photodetector, we saw the pulse get shorter and shorter. We eventually got the pulse down to around 5 nanometers which is pretty close to the specs. Tomorrow, I'm going to set up the power meter that Dr. Cohen got me and measure the average power of the laser.

Wednesday 6.15.2011

We we had our first LTC luncheon today. Rich Migliaccio owns an optical consulting firm, East Coast Optics, and he came to talk to to us about his experiences in the industry. He talked about how the things that he learned from his high school and undergraduate career came into play as he made his way through different industries and jobs. It's reassuring to find out that the things that we learn really are useful. He also talked about all of the different knowledge bases that uses at his consulting firm. They not only include optics, but also mechanical and electrical engineering, and modelling.

After lunch, I compiled a list of things that I would need to build a dye laser and talked to Dr. Noe and Dr. Cohen about what would go in to making this dye laser. Dr. Cohen locaed a cuvette for me to use and hopefully we will be buying the dye for me to make the dye laser soon. I have to figure out a lot of things before I can build the laser though. In order to make sure that there is lasing I have to figure out the power of the nitrogen pump laser and I also have to figure out what kind of reflectivity I need in the cavity in order to reach the threshold for the dye. Currently, I'm trying to research the applications of dye lasers to try and figure out what direction to take this project besides just building the laser.

Tuesday 6.14.2011

Today, we spent the morning researching our own things. I didn't really find anything that caught my eye. It seems that after a couple of days I've exhausted a lot of my resources. Dr. Noe says that I should just start tinkering with making a dye laser and that maybe that will turn in a differnt direction and lead me to a project. At this point, I think that just reading articles is not getting me any closer to a project so I want to get to the point where I can make a dye laser and then figure out something more from there.

Today is Tuesday so we also had our first REU lunch which was a tour of the accelerator labs and the Van De Graaff machine. Rich gave us a full tour and showed us the ion source and the Van De Graaff and even told us all of their histories. We also looked at the old machines from old experiments. He also told us that we could come back to their lab when they're making dip and dots out of liquid nitrogen!

After lunch, we did some more research and Lauren and I decided to go and take a look at the Science and Engineering library because we had both found that there were some resources we wanted to look at there. I had found a book on laser welding online that sounded pretty useful but when I got the book I found that it was way to technical and I couldn't really understand a lot of it, which is not too surprising considering I know every little about laser welding.

Monday 6.13.2011

In the morning, I worked on getting my journal up and running. I decided that the easiest way to go about learning how to create my journal page would be to look at the source codes of past journals. I also found this neat program notepad++ that allows you to write in html code and then it allows you to look at what your page will look like on the internet. This is a compiled list of commands and coding that I learned yesterday.

• html : is something that tags this file as an html file and it goes at the very beginning and end of the document
• head : things in the header tell you information about the file but wont actually show up on the webpage
• body : goes around what you want to show up on the webpage
• table : creates a table to put your text in (in this case I created a table to put all of the text into a smaller column on the page)
• h1, h2, h3, h4, h5, h6 : are six differnt headings
• hr / : horizontal rule
• p : goes at the start and end of each paragraph
• ul : list
• li : goes at the start and end of each list item

I also stumbled upon nanolasers which sound really interesting. They are other wise known as spasers (Surface Plasmon Amplification by Stimulated Emission of Radiation). These lasers make use of sufrace plasmons to create super small lasers. Usually laser size is limited by the cavity size which must be at least half a wavelenght. However, by making use of surface plasmons, labs have created lases that are only a few microns long. A lot of people are saying that these tiny lasers are going to be the key for the next generation of computing and engineering.

Then Dr. Cohen came in today to talk to us about our different projects. I told him about the dye laser that I had made in class last year and he asked me how I knew whether it was actually lasing or the diffraction grating was just picking out the colors that the dye was emitting. Dr. Cohen said that one way to test that its a laser is by putting a double slit in front of it and seeing if it produces the appropriate interference pattern.

After the commuters left, Tom came in and Dr. Noe had us busy working on a derivation of the equation of motion for a pendulum. We found out that if we applied the small angle approximation, the equation of motion for a pendulum is just the equation for simple harmonic motion.

Friday 6.10.2011

Today, I started by taking a look at the dye laser that we have in the back room. I tranced the path of the light around to try and figure out how this particular dye laser works. Dr. Noe told me that the path that the light takes around the cavity is called a bowtie configuration because it bounces around in the shape of a bowtie. There was a lot of optics in the laser and although I didn't know exactly the name and functions of all of the peices and lenses, I could figure out how each piece fit into the general principle of how a dye laser should work, which was really exciting.

We all did a lot a reading to try and find summer projects to do. I stumbled upon some articles about lasers and plasma. There are things called plasma lasers with pump plasma to create extremely intense lasers. But what really caught my eye was the laser generated plasmas. Certain short wave lasers (like continuous CO2 UV lasers) ionizes the air around it and creates a thin layer of plasma around the beam. I read an article about how this property of lasers poses a problem in material welding. The plasma acts as a barrier between the laser and the material and so reduces the efficiency of the laser as a plamsa. There has been ongoing research on how to lower the plasma density between the laser and the material. Some research has found that adding a magnetic and electric field around the area will reduce the plasma density.

Thursday 6.9.2011

This morning we learned the basics of how to work in Linux and html and we got started on how to edit our journals and websites. Some of the basic commands that we learned in html are:

• ls -l : lists all of the files in that directory
• cd : change directory
• pico : opens the file editor
• cntr x : exits from pico

I'm sure that I'll more commands in the future as I become more adept at developing my website!

After lunch, we looked we went to the physics library to do some individual research in what we are interested in. I looked at dye lasers and started gathering more information on how lasers work and more specifically what makes dye lasers so interesting. I found out that the basic principle behind getting a laser to work is creating a population inversion where more atoms are in an excited state than in the ground state. In lasers, this is acheived by using atoms that decay from a short lived excited state to a longer lived metastable state. The transition from the metastable state to a lower excited state is the lasing transition. What a photon passes through these excited atoms, it creates stimulated emission and all of the atoms start decaying from the metastable state to the excited state. Stimulated emission creates a beam of photons, all of the same frequency, moving in the same direction. Then, the key to lasing is having cavity that bounces back the light to create resonance and amplifies the intensity of the light.

A dye laser is just a special type of laser that can create a broad range of frequencies. This is because the dye molecule is very complex and from the excited metastable state, the molecule has many closely spaced lower excited states that it can decay into. The dye must be pumped into a population inversion. Since a laser always lases at longer wavelenghts than it is pumped with, the dye laser must be pumped with something with a short wavelength (often a UV nitrogen laser). The neat thing about dye lasers is that, we can tune them to whatever frequency we want. We just have to add something that will pick out a single frequency and drive that single frequency into the cavity and now the laser will only lase in that frequency. But how do we pick out a single frequency? We can just use a diffraction grating as one side of a parallel mirror cavity and if we position the grating just right, we can get the dye to lase at just one of its range of frequencies.

If I have time, I'm hoping that I can build my own dye laser and play with a couple of different types of dyes, which I think will be a really good learning experience. But tomorrow, I'm going to really crack down on getting some project ideas going and getting some creative juices flowing.

Wednesday 6.8.2011

Today, we gave the guys a chance to figure out how a pinhole camera works. And while they were doing that, Lauren and I played with some of the lenses. After lunch, the guys left and we worked on the problem of why we couldnt focus the lenses with the larger focal lengths into small points of light. We figured out this mystery by, first of all, establishing that the point of light was not just a point of light at all but an image of the sun, and the making some careful ray diagrams using the sun as the object. When we did this, we found that, similar to the pinhole cameras, image size is proportional to the distance between the screen and the lens. This is why when the focal length of the lens is larger, the image that it projects will also be larger.

We also did an experiment using the lenses and the lamp that we have in the lab. We found that there are two distances between the object and the screen where the image will focus. However, if the object and the screen get too close, the lens becomes unable to focus the image. We derived why this is using some simple algebra.

We've been learning a lot about optics by figuring out how and why some phenomenon happen but I'm eger to start reading more articles and figuring out what I'm going to do for my actual project.

Tuesday 6.7.2011

Today was my first day at the Laser Teaching Center. We did a lot of talking and observing and review of general optics principles.

One of the first things that we went over was the difference between a virtual and real image by taking a look at plane mirrors and the pigs. A plane mirror creates a virtual image because the light diverges from the mirror and don't actually form an image. We see an image as our eyes trace the path of the light backwards and that is why the image we see from a plane mirror seems to be behind the mirror. On the other hand, the pigs are a real image. The light is reflected twice on concave mirrors and the mirrors are designed in such a way that the focal length of one mirror is along the other one. As the light from the pigs leave from the focal point of one mirror, they are reflected back parallel and then reflected to the focal point of the second mirror where a real image is formed. We also observed that when we shined a laser beam at the real image of the pigs, it really showed up because the laser beam follows a path down the mirrors to land on the pig and then back up to form a real image of the light shining on the pig.

We also looked at conic sections and learned that light eminating from one focal point of an ellipse will converge at the other focal point. We then took this concept and looked at parabolas. Because the second focal point of a parabola is infinately far away, we found that if there is a source of light at the focal point of the parabola they will be reflected back as parallel rays.

Dr. Noe also talked about the biology of the eye. We were talking about sphereical lenses and how the image is extremely warped at the edges of the sphere. However, the eye has cleverly evolved so that there is a varying index of refraction that reduces this warping of the image as it passes through the spherical eye.

Then we went outside to play with lenses and pie pans. We burned black paper by focusing the light through lenses and some people were even able to burn their names into the paper. We then looked at lenses with longer focal lengths and found that while we could get a focused image through these lenses, we couldn't get a small spot of light like we could with the smaller lenses. We also looked at small pin holes through pie pans. When we help the pans the same distance away from the screen, we found that the spots they made were the same size. However, the smaller pin hole resulted in a dimmer and sharper image as compared to the image formed by the larger pin hole.

We then took all of the observations we made and went inside to try and figure out why we observed what we did. After everyone else left, Lauren and I were left to try and figure out the mystery of the pin hole. After some hard thinking we figured out that it was not diffraction that caused the enlarged image but simple geometry. Using Young's Law, we figured out that diffraction has a small, almost negligible, effect on the size of the image. Simple geometry, however, explains exactly what is going on with the pin holes. A larger spot allows more light in - hence the brighter image, but it also allows a light coming in from a larger angle to pass through which causes the fuzzier image. Geometry also explains why the image becomes larger as the distance between the screen and the pin hole increases.

That was all for today, but tomorrow we still have to figure out why the lenses with the larger focal lengths created a larger spot and not a small dot of light.