Lenses and the “Bending” of Light
Day #1 - Refraction
Let’s briefly review what we know about light. First and foremost, light travels as an
electromagnetic wave. Secondly, whether we are talking about Radio waves, microwaves,
ultraviolet, waves, or the visible light spectrum ROYGBIV, they are all light. Therefore, some
light has a higher frequency than other light (gamma vs. radio for example) and some light has a
longer wavelength than other light (infrared vs. ultraviolet, for example). Thirdly, and most
importantly, we learned that all light travels at the same speed when it travels through a vacuum.
This speed is 300,000,000 m/s, or 3 x 108 m/s. Since a vacuum consists of “nothingness”, there
is nothing to slow light down, and it moves its fastest in a vacuum.
Now for our current chapter. When light passes from one medium (or substance) into another, it
changes direction. This is known as Refraction. Some materials are optically “denser” than
others. For example, air is less optically dense than glass, which is less optically dense than
diamond. This term, “Optically Dense” is used to refer to a medium in which the speed of light
changes. For example, since a vacuum is not “optically dense” at all, light travels very fast
through it. However, when light travels through diamond, which is much more “optically
dense”, it will slow down. When a light ray slows down, it bends. If you look at the first picture
below, it shows incident light striking a glass surface. Notice that some of the light was reflected
(following the law of reflection, that says that the two angles are the same). However, some of
the incident light travelled through the glass. Since it was travelling in air, and now it’s
travelling in glass, the light slowed down. This caused the light ray to bend (or refract). Now
look at the second picture, which shows light travelling through glass into water. Water is less
“optically dense” than glass. Therefore, the speed of the light changes, and the light refracts (or
bends). However, since it speeds up, it bent the other way.
Reflected
ray
Incident
ray
Incident
ray
air
glass
LHT
Refracted
ray
Reflected
ray
glass
water
HLA
Refracted
ray
What does “LHT” mean? Its an easy way to remember which way the light bends when it enters
a new medium (or substance). If the light travels FROM a lite (intentionally speeled wrong to
avoid confusing it with the word “light”) medium INTO a heavy medium (in other words, from
less dense to more dense), then the light bends TOWARDS the normal. Hence
Lite into Heavy bends Towards the normal (LHT)
On the other hand, if light travels FROM a heavy (or dense) medium INTO a lite (or less dense)
medium, then light bends AWAY from the normal. Hence
Heavy into Lite bends Away from the normal (HLA)
So…..the question should be, “What makes something more or less optically dense than
something else”. We measure a medium’s optical density using a ratio known as the
INDEX of REFRACTION, or “n”. It is the ratio of the speed of light in a vacuum (again,
3 x 108 m/s) to the speed of light in a given material. Thus, the index of refraction is given by
(where c is the speed of light in a vacuum and v is the speed of light in the new
material)
If you look at the table at the right, you will see the index
of refraction for some common substances. The larger the
index, the more light is slowed down, and thus the more it
is bent. This can be seen on the following pictures…
vacuum
air
vacuum
water
vacuum
quartz
Just a reminder, since all of the pictures above show that
Medium
Index of Refraction
vacuum
1.00
air
1.003
water
1.33
ethanol
1.36
fluorite
1.43
polystyrene
1.49
crown glass
1.52
quartz
1.54
Zircon
1.92
diamond
2.42
light travels from a vacuum (less dense, Lite) into something else (more dense, or Heavy), the
light bends Towards the normal. Hence LHT. On the other hand, the refracted light would have
bent AWY FROM the normal if the incident light travelled from heavy into lite (hence, HLA).
OK, so hopefully we see that light bends when it travels from one substance (or medium) into
another substance. But “HOW MUCH WILL IT BEND???” We know two things.
#1) The refracted ray bends more if the indices refraction of the two different
materials are far apart. Hence, light travelling from fluorite into quartz only bends
a little (since the indices are 1.43 and 1.54), while light travelling from ethanol into
zircon bends a lot (since 1.36 and 1.92 have a larger gap between them).
#2) The actual “angle of refraction”, the angle between the normal and the
refracted ray, can be found using a law called “Snell’s Law”.
Snell’s Law:
Incident
ray
Reflected
ray
Incident medium (n1)
Refracted medium (n2)
Refracted
ray
So, let’s review. Light bends. When it travels through a vacuum, it travels at the speed of light,
3 x 108 m/s. Since the index of refraction of air is VERY close to that of a vacuum, light travels
at approximately 3E8 m/s through air. When is enters a medium that is more optically dense
(water or glass, for example) it will SLOW DOWN and bend towards the normal. This would
mean that the angle of refraction would be LESS than the angle of incidence. If light travels
from one medium into a less dense medium (whose index is smaller), then it SPEEDS UP and it
BENDS AWAY from the normal (thus making the angle of refraction greater than the angle of
incidence).
Refraction Worksheet
1. Using the table on the previous page, find
the speed of light in fluorite.
2. What would the index of refraction be if the
speed of light through a certain material
were 1.73 x 108 m/s?
3. What is the minimum value of the index of
refraction? Explain your reasoning as to
why this must be true.
4. Light travels from quartz into water. Will
the light bend towards the normal or away
from it? Fully explain why?
5. Light travels from air into crown glass. If
the incident angle is 50o, use Snell’s Law to
find the angle of refraction.
6. A ray of incident light (with an angle of
incidence of 60o) leaves Zircon and enters
an unknown medium. It bends away from
the normal with an angle of refraction of
80o. Use Snell’s Law to find the index of
refraction of this new material.
7. Red light, of wavelength 700nm
(nanometers), is travelling through the air
when it encounters a diamond surface. If
the frequency of the light never changes,
find the wavelength of the light as it passed
through the diamond, using both the wave
equation and the equation for the index of
refraction. (
)
The minimum value is 1. Since v = c/n, if n was
less than 1, then the velocity of light in that
material would be faster than the speed of light in
a vacuum. Since a vacuum offers no resistance to
light, 3E8 MUST be the theoretical maximum for
light’s speed, and therefore, “n” CANNOT be less
than 1.
Quart is high-index (optically heavy). Water is
low index (optically light). Therefore…HLA!
The refracted light will bend AWAY from the
normal.