# Classroom experiments and activities

## Determination of the index of refraction using a laser pointer

### Determination of the index of refraction using a laser pointer

Grzegorz F. Wojewoda
I High School
Bydgoszcz, Poland

The advent of low-cost lasers, like laser-pointers or laser-levels, allows us to experimentally verify in classrooms values of refractive indices quoted in textbooks! We have prepared 2 exercises in which students can measure a value of a refractive index by themselves with use of a diffraction grating and a polarizer.

Warning!
Never put the laser beam in direction of eyes!
Laser beam can permanently damage vision!

 Measuring index of refraction

A. Measuring refractive index with use of diffraction grating

1. Required materials

For conducting experiments you will need the following:

• laser pointer (alternatively laser level),
• diffraction grating with 200 to 500 lines per 1 mm. You can use a grating made of CD disc - see description of a home-made spectroscope on the HOU website, but making use of low-cost gratings will give better results. In Poland, we acquire such gratings from the ZamKor publishing house, http://sklep.zamkor.pl/ ,
• transparent vessel,
• two clips for hanging clothes,
• adhesive tape (the best will be an insulating tape),
• scissors,
• tracing paper (or any other semi-transparent paper),
• book (to be used as a stand for laser).

 Fig. 1. Parts of experimental setup

2. Realization

Cut a part of a tracing paper with scissors and stick it to one of the external walls of a vessel. To the opposite wall stick a diffraction grating. The higher number of slits per 1mm in a grating, the bigger is the angle at which an interference pattern will be visible (one can have doubts about a possibility of comparing values of sinus and tangent of the angle at which the pattern is visible). Nonetheless, the obtained pattern shall be sharper, so defining its location will be easier.

 Fig. 2. Preparation of a vessel for an experiment .

Into a ready-made vessel pour water or other liquid which refractive index you want to measure.

 Fig. 3. Vessel filled with a liquid

Place laser in such a way to make its beam go through the liquid and mark on the screen location of a zeroth order fringe and two fringes of the first order.

 Fig. 4. Position of laser with respect to a vessel with liquid

Change the height of laser to make its beam go above the liquid surface. Again mark location of interference fringes.

 Fig. 5.  New position of laser with respect to a vessel with liquid

3. Results of an experiment

Distances between the first order fringes marked on the screen should be shorter when laser beam goes through water than when it goes through air. It is better visible when you use a laser level (a product available in construction shops) instead of a laser pointer.

 Fig. 6. Experimental setup with a laser level

 Fig. 7. Differences in location of interference fringes when light passes through water and through air

4. Elaboration of experimental results

Bright fringes of the first row meet a requirement:

 - in the air:

 - in the water:

From geometry of the experimental system:

 in the air: in the water:

We can make use of approximation of small angles:

So length of light waves:

 in the air: in the water

Refractive index of water relative to air:

where:
 - speed of light in the air - speed of light in the water

Final value of refractive index of water relative to air follows:

According to our measurements, value of refractive index of water is 1.29. The value does not diverge much from values listed in tables, that is 1.3.

B. Measuring refractive index using a polarizer

1. Required materials

To set up experiment you will need the following:
• laser pointer (or laser level),
• linear polarizer (you can use polarizer distributed by the ZamKor publishing house, but you can also use polarizer obtained from a calculator display or mobile phone display),
• glass pane, which refractive index you want to measure (you can use any polished dielectric),
• angle-meter,
• clips for hanging clothes,
• adhesive tape (the best will be an insulating tape),
• white paper (to be used as a screen),
• books (to be used as stands for experimental systems),
• a lot of patience .

 Fig. 8. Parts of experimental setup.

2. Realization

If you don't have a ready-made polarizer you can obtain it from a calculator or mobile phone display (the process of obtaining polarizer will destroy a device irreparably, so it is recommended to use for that purpose a device that is definitely out of order). For that purpose you shall disassemble a display and remove from it two polarizing foils.

 Polarizing foils obtained from a calculator display

With use of clips for clothes put a glass pane under research vertically. Put an angle-meter under the glass pane. A bottom edge of the pane shall ideally coincide with the line defined with use of the angle-meter.

 Fig. 9.  Placement of glass pane on an angle-meter

Put laser on the second book and illuminate a glass pane with laser so that it was possible to see incident and reflected rays. Books are very useful for that purpose since you can change a number of pages on which optical devices are placed and precisely regulate their mutual setting.

 Fig. 10.  Illumination of a glass pane with laser

Put a line polarizer on the way of a reflected ray in a way which allows for its free rotation around the axis parallel to the ray of light reflected in the glass pane.

 Fig. 11.  Placement of polarizer in relation to the reflected ray

Light reflected from a glass pane is partly (and in a particular case fully) polarized. Our task is to obtain such a setting of an angle of light incidence to a glass pane and such a setting of a polarizer so that a reflected light did not go through a polarizer! Search of such setting requires a lot of patience and attention. When you succeed, you can assume that light reflected from a glass pane is fully polarized. An angle of incidence at which reflected light is fully polarized is a result of the experiment.

 Fig. 12.  Image of light reflected from a glass pane visible on a screen

3. Elaboration of experimental results

At the border line of two dielectric materials we deal with partial reflection and refraction of light. When there is an angle of 90º between a reflected and refracted ray, reflected light becomes polarized linearly. An angle of incidence which meets that requirement is known as the Brewster's angle. Relation between the Brewster's angle and refraction index is the following:

It means that in our experiment we are not interested in a refracted ray, but in a reflected ray. So the thickness of dielectric from which a fully polarized ray is reflected is of no importance. Therefore, that method can be used to measure a refractive index for a non-transparent dielectric.