Using the Refractometer
to measure Refractive Index

As a ray of light passes from air into a block of glass, the direction in which it is travelling is changed. The path is bent.
The amount of bending that takes place depends on the nature of the glass and the wavelength of the light being used. In all these investigations the yellow light emitted by sodium ions is used. It has a wavelength of 589 nanometers.

Tools of the Trade

Brother Gregory's refractometer is very simple. He has provided you with many different samples of glass blocks; the same types of glass used to make the microscope lenses. He has also given you two lights; a blue, reference, light which shines straight through the glass block and shows you the position of the "normal".
The second, yellow sodium light (589 nm), is the source of the light used to make the measurements. It is this light that shines at an angle to the surface ot the block of glass, and whose path is bent, allowing you to find the refractive index of the glass sample.
He has also provided you with a light detector, that is used to find where the yellow light leaves the glass block.

Taking a Measurement

Use the illustrations below, to step through the procedure necessary for measuring the angles in the refractometer, and determining the refractive index of the glass.
(Move your cursor over the "buttons" on the left).

Taking a Measurement

One


Two

Three

Four

Five

Six

Seven

Eight

Nine

Ten

Eleven


Recording the results

For each measurement, record four values, two for the source light and two for the image;

Source Light Settings 
Image Output Results 
Distance from reference light 
Distance from glass 
Thickness of glass 
Image distance from reference light 
Your results go here 
Your results go here 
Your results go here 
Your results go here 
HELP  from Mendel's Mother
Print out this special
"Results Table", and use it to record your results.

Calculations
Triangles

All the calculations necessary for finding the refractive index of a piece of glass depend on the geometric properties of a right angle triangle.
In a right angle triangle, one of the three angles is at exactly 90 degrees (a "right angle"). The other two angles in the triangle are both less than 90 degrees.
The side of the triangle opposite the right angle is called the "hypotenuse".
A mathematical quantity called the "Sine" of an angle (in a right angle triangle) is a simple ratio of the distance along the side of the triangle opposite to the angle, to the distance along the hypotenuse.

Pythagoras

The size of all the sides in a right angle triangle have a simple relationship to one another.
The size of the hypotenuse multiplied by itself ("squared"), is equal to the sum of the squares of the distances of the other two sides.
(hypotenuse)^{2} = (side one)^{2} + (side two)^{2}
This is called "Pythagoras' Theorum".
Therefore, if you know the size of any two of the sides of a right angle triangle, you can always calculate the size of the unknown side.

Two Triangles

There are two important right angle triangles involved in determining the refractive index of a block of glass.
A ray of light from the sodium source is the hypotenuse of one right angle triangle (in the air), and the same ray of light forms the hypotenuse of another right angle triangle in the glass.
The angle made by the ray of light in the air to that of the reference light (the normal), is the angle of incidence, and the angle made by the ray of light in the glass to the same normal, is the angle of refraction.
It is the ratio of the sines of both these angles that is the refractive index of the block of glass.
The calculation is preformed in three steps:

Step One:
Distance traveled
by light rays

The first calculation determines the actual distance traveled by the ray of light in the air and in the glass. This is the hypotenuse of the two right angle triangles.
Once again, a table makes the calculation easier.

Distance traveled by ray in air
distance from reference light
DR 
(distance from reference light)^{2}
(DR)^{2} 
distance from glass
DG 
(distance from glass)^{2}
(DG)^{2} 
(distance from reference light)^{2}
+ (distance from glass)^{2}
(DR)^{2} + (DG)^{2} 
square root of
(distance from reference light)^{2}
+ (distance from glass)^{2}
sqrt [(DR)^{2} + (DG)^{2}] 
20 
400 
34 
1156 
1556 
39.446
distance travelled
by ray of light
in the air 

HELP 
from Mendel's Mother
Print out these special tables:
"Calculation Table One"
"Calculation Table Two", and use them to calculate your results.

Now do exactly the same calculations to determine the distance traveled by the ray of light in the glass; the second hypotenuse of the second triangle.

You can use
Brother Gregory's
Triangle Calculator
to find the lengths
of the triangle sides.


Step Two:
Calculate the sines
of the angles

Using the distances just calculated for the distances traveled by the ray of light in the air and in the glass, and the "distance from the normal" (in the air) and the "thickness of the glass" (in the glass), it is now possible to calculate the sines of the angle of incidence and the angle of refraction.

Sines of angles
Sine: Angle of Incidence 
Sine: Angle of Refraction 
distance traveled by ray in air 
distance from reference light 
distance from reference light
distance traveled by ray in air 
distance traveled by ray in glass 
image distance from reference light 
image distance from reference light
distance traveled by ray in glass 
put your results here 
put your results here 
put your results here 
put your results here 
put your results here 
put your results here 

Step Three:
Calculate the
refractive index

The final step in the calculation sequence is to determine the ratio of the sine of the angle of incidence / sine of the angle of refraction.
n = Sine I / Sine R
Where n is the refractive index
Sine I is the sine of the angle of incidence, and
Sine R is the sine of the angle of refraction.

You can use
Brother Gregory's
Sine Calculator
to find the Sine values
of both the triangles.


Record your results

For each sample of glass tested, write down your results in the form of a set of tables (like the ones used above).
HELP 
from Mendel's Mother
Print out this special table:
"Calculation Table Three"
and use it to calculate your final results.
For each sample of glass, measure and calculate the refractive index at least three times.
Make sure that you keep good records, you will need the values you have found for these glass types later.

Use the Refractometer
begin using the refractometer to find the refractive index of Brother Gregory's blocks of glass.
