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