You know the lenses that are referred to as high-index? Or do you have stock lenses that are referred to as the manufacturers 1.6 or 1.66 lenses? Well, the term high-index and the numbers like 1.66 are references to the index of refraction of the material that the lens is made from.

The Index of Refraction is a shorthand way of discussing how dense the lens material is, or how fast the light ray is traveling when it goes through the lens.

Did you notice that I used those terms quite a bit in the last section when I discussed the angles? I kept referring to the density of the material or the speed of the ray of light in the material. We want to be able to easily compare the speed of light in several different materials.

Last week we discussed the speed of light in a vacuum and in several other materials. In a vacuum, light travels 186,000 miles/second, or 3x10 meters/second.

We are going to discuss each lens material by comparing the speed of light in the material to the speed of light in a vacuum. To do this, we will form a ratio of the speed of light in a vacuum to the speed of light in the material.

In crown glass light travels at 122,000 miles/second. If we create a ratio of 186,000/122,000, we have 1.52. So we will say that the index of refraction of crown glass is 1.52.

How about CR39, the most common lens material in the United States? The speed of light in CR39 is 124,000 miles/second. Slightly faster than crown glass, isn't it? If we create the same ratio, speed of light in a vacuum / speed of light in the material, we get 186,000/124,000 = 1.50.

The speed of light in crown glass was slower than in CR39, and the index of refraction of crown glass was slightly higher than CR39.

How about that stock lens that is called [brand-name] 1.66? Well, the 1.66 is the index of refraction of the material. If:
                                   speed in vacuum
index of refraction = ------------------------------
                                   speed in material
then we have
                  186,000 miles/second
       1.66 = ------------------------------------
                     speed in material
and so
                                         186,000 miles/second
            speed in material = -----------------------------
                                                   1.66

  speed in material = 112,000 miles/second.

Again?

Well, at least we see that this nice material that gives us such thin lenses really slows the light down. The higher the index of refraction, the slower the light goes in the material.

OK, read page (22 / 27-28) in the textbook. Then we will do a few more.

We have two forms of this equation. If you were comfortable with the ratios and solving the equations in the math class, then you only need to remember one of them. If not, remember this: For index of refraction questions, divide 186,000 by whatever you are given. The answer is what you were asked for!

So, if I tell you that polycarbonate has an index of refraction of 1.586, and I want to know what the speed of light is in it, you will warm up your trusty calculator, punch in 186000 / 1.586 = and you will see 117276.... which we will round to 117,000 miles/second. [Why are we rounding? Because the value that we are using for the speed of light in a vacuum is correct to the thousandths place, so our answers will only be correct to the thousandths place.]

On the other hand, if I tell you that light travels at a speed of 76,000 miles/second in a diamond, you will punch 186000 / 76000 = into your calculator and you will get . . . 2.4473... which we will round to 2.45. Are you doing these with me, or are you just absorbing the lecture like you were watching TV?

Do this one: A material has an index of refraction of 1.33. How fast does a light ray travel in it?

Or, light travels at 109,000 miles/second in a particular flint glass. (It is sometimes used in the reading part of glass bifocals.) What is the index of refraction of this particular flint glass?

Did you get 140,000 miles/second for the first one? And did you get 1.71 for an index for the flint glass?

By the way, the index 1.33 material is water. ;-)

OK.  Reread page (22 / 27-28) in the Optical Formulas book, do the exercises on page (23 / 29), and check those answers in the back of the book.