# Optical Instruments

by Jared Rovny

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00:01 We have an understanding now about how lenses and mirrors behave as well as a few different properties of lenses and mirrors and how to measure those properties. We’re ready now to apply the things that we learned in lenses and mirrors to some specific optical instruments as well as to some real world scenarios. The first thing we should know is that there’s a measurement of the power of a lens that we can measure which is defined as 1 divided by the focal length of that lens. If we remember that for a circular lens that has a particular circular curvature, a particular radius, the focal length was at half that radius. We could plug in that particular value for the focal length into this equation for the power here and then rearrange, 1 over the radius over 2 will be equal to 2 over the radius. This is another way to measure the power for a circular lens. This unit of power, as you can see just by looking at the equation is in 1 divided by a distance unit, whether it’s the radius or the focal length. These are distances and so the units of power are 1 over distance which we call diopters. These units of diopters are called again the power and it turns out that this power is also proportional to the index of refraction of our material.

01:18 We’re very much used to using things like glasses. So, the index of refraction won’t change much for that material in particular. But it is good to know that we could use a different material with maybe a higher index of refraction to increase the power of our lens. If we have more than one lens, so for example, if we have a couple of lenses like this, we put them next to each other and use them together, the way we add the power for the two lenses together is simply to add them linearly exactly like we have here. So, the total power of two lenses together will simply be the sum of the power of the first lens and the power of the second lens. Then of course, we could use our definition for the power of lens, 1 divided by the focal length for that lens and then see a new equation for the total power as 1 over each focal length of the lenses added together.

02:07 The magnification is a second property for a lens and for two which we’ve already discussed.

02:13 But for two lenses as we have here, if we wanted to add them together, it turns out that the magnification for these two lenses multiplies. So, this is slightly different than for the power.

02:24 So, we have these two equations for adding lenses but for the magnification which again is slightly different, we could for example, have a one lens with a magnification of 2 put next to a second lens with a magnification of 3. In this case, we would have a magnification not of 5 but of the product, 2 times 3 which is a magnification of a 6. Be careful with the idea of power and of magnification. Keep them separate especially when you’re adding lenses together. There are few properties of real lenses that we have to account for. One of which is the aberration in your lens. We’ve made some assumptions about how lenses work especially assuming a very nice geometrical model where we have these particular rays. They always follow the geometric laws that we’ve given to them. But in real life, this isn’t always the case.

03:11 We could always have some problems in our lenses. This can cause aberrations. In which case, when light is coming towards your lens and tries to meet at the focal point on the far side of your lens, all the light rays don’t necessarily meet. They don’t necessarily behave and do what we were expecting them to do. When this is caused by the color of the different types of light that are coming into your lens, we call it the chromatic aberration. We call it chromatic, meaning the color of the light where again we talked about how different colors of light, maybe red and blue can bend and refract differently than each other as they’re going through a material.

03:48 This is in contrast to the first kind of aberration we just introduced which didn’t have anything to do with the light color. Therefore, we call that first one the monochromatic aberration since it could happen even if the entire light was of the same color. We have one color, so it’s monochromatic aberrations. These kinds of aberrations, whether they’re monochromatic or chromatic can be corrected. We can put in some extra sort of corrective features to our lenses to try to correct for aberrations and get the light going back towards that focal point. It’s not necessarily important for us to memorize many different methods of correcting for aberrations aside from just the idea of putting something behind our lenses we have here. What is important to know is that there can be aberrations for a number of reasons including just because our model isn’t exactly perfect and also because of the color of the light behaving differently as it refracts through a material.

The lecture Optical Instruments by Jared Rovny is from the course Geometrical Optics.

### Included Quiz Questions

1. It can be increased with decreasing focal length.
2. It can be decreased with decreasing focal length.
3. It can be increased with increasing focal length.
4. It is independent of focal length.
5. It is equal to the inverse squared of the focal length.
1. Power doubles, magnitude squares
2. Power squares, magnitude doubles
3. Power halves, magnitude doubles
4. Power doubles, magnitude halves
5. Power doubles, magnitude doubles
1. Chromatic aberration depends on the color of the light; monochromatic does not
2. Monochromatic aberration depends on the color of the light; chromatic does not
3. Chromatic aberration depends on the amplitude of the light; monochromatic does not
4. Monochromatic aberration depends on the amplitude of the light; chromatic does not
5. They are the same unless the lens is diverging

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