Refractive index

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Definitions

The refractive index of a substance is usually quoted for a given wavelength of light. Often the sodium "d" lines.
It is a ratio of the speed of light in a vacuum to the speed in the medium. Thus the value is always greater than 1.

refractive index,n = Speed of light in vacuum/speed in medium

More often than not you will be dealing with light going between two media, for example air and glass. The use of subscripts then illustrates the media changes. It reads from left to right, numbers or letters are used depending on the author's whim.
e.g. Refractive index of air to glass is ang It follows that ang = 1/ gna. The good news is that if air and glass or acrylic are used the speed in air is close enough to vacuum for the absolute value to be used.
However it is easy to convert if both absolute values are known:
e.g. ang = (Speed in air/ speed in vacuum )x (speed in vacuum /speed in glass) which can cancel out common terms...
ang = (Speed in air/ speed in vacuum )x (speed in vacuum/speed in glass) to become...
= (Speed in air/speed in glass)
= (1/nair)x(nglass)

Two methods are commonly used to measure refractive indices in school.

  • 1 The comparison of angles of a beam of light either by pins or from a raybox.
  • 2 The apparent depth method

As consequence of the refractive index total internal reflection can occur. This is usually measured with a semicircular block and rays of light

The Measurement of Refractive index of a block by ray tracing

Apparatus:

  • Glass or acrylic block
  • Pencil
  • paper
  • protractor
  • Light box and power supply or optics pins and pinboard
Ray tracing for a glass block

A block of glass or acrylic is placed on a piece of paper and light shone through the block.
The outline of the block is traced onto the paper.
The path of the ray is marked on the paper too. (If no ray box is available the path can be shown by lining up optics pins as shown. They should be in line when viewed from the emerging side).
Note the ray under the block should also be drawn. This can be inferred as the line between the ray entering the block and the ray leaving.
A normal (construction line at 90 degrees) is marked where the light enters the block.
The angle if incidence, i, is noted. The angle of refraction is also noted, r.This is the angle between the internal ray and the normal.
A calculation is made for the value of the sine of these pair of angles.
The process is repeated for several values of incident angles.
A table is drawn up and this should show n= sin(i)/sin(r)

  • Snell's law: n= sin(i)/sin(r)

The Measurement of Refractive index of a block by apparent depth

Diagram of the method for determining refractive index by apparent depth
  • Glass or acrylic block
  • 30cm rule
  • Cork if required
  • Boss clamp and stand if required

An optical pin is placed beneath a block of glass.
An identical pin is moved up and down until it appears to be at the same depth. This is checked by moving the head so as there is no paralax between the virtual pin and the real pin at the side of the block.

N.B. The diagram shows the pin to one side, this is for clarity of measuring. The real pin would be in line with the one below the glass block. The test pin may be mounted in a cork and the cork raised until the required height is reached, using a boss and clamp. The two depths, real and apparent, are measured.
The refractive index, n is the ratio of the real depth/apparent depth. The above process can be used for liquids. In this case the use of a mirror and the reflection of the test pin located above the surface of the liquid is used. A small error correction is made for the difference in height of the mirror and liquid surface. This method has gone out of favour and is only included for reference.

This method can be adapted to measure refractive indecies of liquids. A travelling microscope (a microscope fixed to a vernier scale) can be mounted so that it measures vertical movement. A shallow container, e.g. a petri-dish may have a mark placed on the top surface of the base. The microscope is then focussed on the mark, and a reading, O, is noted. From now on the telescope's focus is not touched. Liquid is introduced into the container,and the telescope is moved so that the mark is again in focus. The reading, A, is then taken. Lycopodium is traditionally put on the surface, although talc powder is also able to be used. The microscope is then moved to focus on this and a reading for the surface level, S, is taken.
Real depth is S-O
Apparent depth is S-A
Refractive index,n, is (S-O)/(S-A)


Measurement of the critical angle in a semicircular block

Critical angle measurement

Apparatus:

  • Semicircular bloc
  • Pencil
  • paper
  • protractor
  • Light box and power supply or optics pins and pinboard

The block is placed onto the paper and positioned so that the the beam of light (or incident ray) goes through the curved face and strikes flat face at the centre.
Moving the block so that light is close to "the normal" will have rays both transmitted from and weakly reflected in the block.
Rays near at shallow angles to the flat face are all internally reflected.
Rays at the critical angle send light parallel to the flat edge as diagram there will also be a reflected ray but this has not been shown in the diagram.

  • Formula for the critical angle: Sin θc= (or more often Sin c) = 1 / n

Refractometer

A refractometer is a device that directly measures the refractive index of a solution. Typically these are hand held devices which cover a specific range of refractive indecies. They employ a telescope type device to analyse a thin smear of liquid. Often they are calibrated in commercially useful scales (e.g. %Brix See wikipedia's article on Brix). These are often used in the food industry where quick, reliable results are required. The calibration is normally specified for a given temperature.

A hand-held refractometer

An American website shows how one may be used in brewing beer (so it can't be all bad!).

Appearing coin trick (demo)

This is a surprisingly convincing demonstration and the use of a flexible camera can make a useful addition.

  • Apparatus:

Rectangular clear tank of about 20cm depth or more.
Coin (or small mass piece)
Water
Flexible camera. -and method for class display.

  • Method:

Actual positioning depends on tank dimensions and a practice run is suggested.
The coin should be placed in the bottom of the tank about midway down the longest length.
Position the camera (so that it will not be splashed) at one end of the tank.
Angle the camera to miss picking up the image of the coin by a few degrees.
Invite the class to view the set-up and see that there is no trickery.
Pour water into the tank and watch the screen as the coin appears.

The “bending of light” can be emphasised by having a glass rod already in water that appears straight. On removal it is shown to be slightly bent upwards. This requires some effort to get the correct angle and will also need supporting to stay in the “correct” position.

Optical matching

Fibre optics are used widely in communication. Getting power efficiently into the fibre can increase the distance communications can be sent withou the need for amplification. Light energy is often lost when there is a change in media- think of the reflrctions from a swimming pool on a bright day. Some substances have a refractive index near to that of glass. These can be used to match glass to the optics housing. There are two demos that show this nicely.

  • Glycerol (propan-1-2-3-triol) is placed into a clear container containing a soda glass rod and a boroscilicate glass rod. The Boroscilicate rod is nearly invisible, whereas the soda glass rod has a clear outline.
  • a glass rod is bent into an elongated "J" shape. The bottom should be reasonably round. Light is shone down the "J" from the long limb. Light can be seen to come out of the short limb.

When the "j" just touches a beaker of glycerol light spills into the beaker and the short limb no longer has any light emitting.

Double refractive indicies

Calcite crystals, amongst a few others exhibit two refractive indices dependant on the polarisation of the light. One is the "ordinary ray" and the other is the "extraordinary ray". Viewing text through a calcite crystal is an easy method to show this.

External links

The following link to Harvard's experiments is suggested as an unusual discussion point. Look in section 3 "Bouncing lightbeam". Harvard demo index. Most lasers will not show this to readilly unless there is a very good blackout. An alternative is a green laser (available through Rapid Electronic for example). However these are dangerous and local prohibitions are very likely to exist. A special risk assessment and control measures will almost certainly be required.
The National Physics Laboratories have produced tables of refractive indecies and are available on line from the Kaye and Laby website


--D.B.Ferguson 22:07, 19 March 2007 (GMT)

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