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- CHAPTER XXI
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- POLARISED LIGHT
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- Experiments on the Polarisation of Light.
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- 349. Apparatus. - The polariscope used in the
following experiments may be easily made of wood. To a base board
about
 6 inches square, attach two uprights, each
about 12 inches high and 3/8 inch by 1 inch section. On the top
of these fasten a stage, EF, also 6 inches square, having a hole
1/2 inch in diameter at its centre. About 6 inches from the top,
fix a horizontal glass plate, D, to act as a platform, and at
about 4 inches from the bottom hinge another glass plate, A,
about 5 inches square. An ordinary silvered mirror, B, about
4 or 5 inches square is placed on the bottom; and a piece of
zinc, Z, is bent round partly to inclose the space between the
platform at the top and the glass stage. The zinc may be attached
to the stand by a sort of bayonet joint, P, so that it can easily
be removed. Cut a hole about 3 inches in diameter in the thin
piece of wood 6 inches square, and fasten this to the top of
the table, EF. The glass plate, A, can easily be hinged by inserting
it in saw cuts made in small wooden blocks as indicated in Fig.
365. Cut a black card to lie on the glass
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TREATISE ON PRACTICAL LIGHT |
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- stage, D, with a hole 1/4 inch in diameter vertically
under the hole in the top board. Draw lines on the top stage,
EF, parallel to the sides, which would, if produced, pass through
the centre of the circles, and also lines bisecting the angles
between these, so as to mark every 45°.
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- Fitting easily in the 3 inch circle of the platform, EF,
make three wooden discs each with a 1/2 inch hole through its
centre, of the same thickness as the board in which the 3 inch
hole was made. To one of these, El Fl,
(Fig. 366), attach two uprights, and hinge between them in the
same way as before, a small mirror, C (Fig. 366), about 1
inch by 1 1/2 inches, either of black glass, or of glass
blackened at the back, with the reflecting surface downwards.
Oil another disc, E2 F2, between two similar
- uprights, support a " pile of plates," T, of micro-cover
glass at an angle of about 53°. The glasses used by botanists,
about 2 inches by 1 inch, answer perfectly for this purpose.
To the third E3 F3, attach a short tube
which just fits a small nicol's N - one of those sold for attachment
to the microscope is sufficiently large.
-
- In addition to the polariscope, two rhombs of Iceland spar
of about 1/2 inch side, a second nicol, and a pair of tourmalines
will be required; protractor, piece of spar cut perpendicular
to the axis mounted in cork ; tinfoil ; two sewing needles stuck
into a wood block with their points outwards and in the same
vertical line.
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- 35O. Use of Polariscope.-(a) Set up the polariscope in front
of window so that the light from the skyl shall be-
-
- 1. Reflected vertically down from the inclined glass plate,
AA (Fig. 367).
-
- 2. Reflected vertically up from the silvered mirror, B.
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- l At night a sheet of white card
may be set up in front of the instrument, with good light illuminating
it.
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- 3. Partly transmitted by the glass plate, AA.
- NOTE.- Nearly all the light is returned by the plate to the
sky, but a small portion is transmitted.
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- 4. Reflected by the black glass plate, C, into the eye.
-
- (b) Without otherwise moving anything rotate the top
black glass round a vertical axis, and observe the effect on
the light.
-
- In two positions the light will be nearly extinguished, and
in two positions it will have maximum brightness.
-
- Draw a diagram to indicate clearly the two positions in which
it is dark, and the two in which it is bright.
-
- Definition.- If plane polarised light be incident
at the angle of polarisation on a glass surface (and the plane
of incidence be varied by rotating the glass while the angle
of incidence be kept the same), the plane of incidence in
which the light is best reflected is the plane of polarisation
of the incident light.
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- 351. Plane of Polarisation. - (a) Examine the light
transmitted by the plate A, and using the above definition, find
its plane of polarisation. Also state, with reasons, whether
the polarisation produced by the plate A was produced by (1)
the reflection down to B, or (2) the transmission through
A.
-
- (b) Replace the black glass mirror, C, by the pile of plates,
draw diagrams as in Experiment 350, and compare them with those
obtained in that experiment.
-
- Show that the planes of polarisation of reflected and transmitted
light are at right angles.
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- 352. Brewster's Law. - Replace the black glass mirror,
and turn
- it to extinction. Now without rotating its plane alter its
inclination, and that of the plate A, until the centre of the
field is quite dark, and thus endeavour to find the angle of
polarisation. Measure this angle with a protractor; and using
the formula given by Brewster:
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- tan i =u ,
-
- find the refractive index of the glass.
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| 452 |
TREATISE ON PRACTICAL LIGHT |
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- 353- Double Refraction. - (a) Examine the small
rhomb of Iceland spar- there are eight angular points; see that
at six of these corners, there are two acute and one obtuse angle,
but at
 the other two, which are diagonally opposite
one another, there are three obtuse angles. If the rhomb has
all its edges equal the line joining these two points is
the optic axis of the crystal. Draw the crystal.
-
- (b) Make a small black dot on a piece of paper, and
place one of the rhombs upon it. You will see two dots. Draw
a diagram of the crystal as seen from above, inserting in the
drawing, the optic axis, and the line joining the
- dots. Notice carefully the relation of these two lines.
-
- (c) Rotate the crystal and draw a diagram of the appearance
every 90°. Which dot moves?
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- (d) Raise the rhomb gradually from the paper, and
notice carefully any change in position of the dots. Does their
distance apart alter? Hence show by diagrams in a vertical plane
the course of the rays to the eye.
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- (e) Set up the block with the two needles so that
their points are vertically over a black dot on a piece of paper
(Fig. 369). Place the rhomb over the dot, and using the needles
as a guide, observe which of the two dots coincides with the
original dot. The dot that coincides is called the one
- formed by the ordinary ray, and the other is formed by the
extraordinary ray.
-
- (f) See that it is the ordinary ray that remains
still when the crystal is rotated.
-
- (g) Look carefully at the apparent positions of the two dots
in
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- the crystal. One will be seen to be higher than the other.
Which is it? Hence which refractive index is the greater-that
of the ordinary ray or that of the extraordinary ray?
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- 354. i. Polarisation by Double Refractiou.- (a)
Make a pin-hole in a piece of tinfoil, and lay it on the stage
of the polariscope (Fig 365). Place a spar rhomb on it, and looking
directly down through the hole in the top stage, observe the
effect of rotating the rhomb. Hence show that the light of each
dot is polarised. Which ray is polarised in the plane containing
the two dots?
-
- (b) Place the rhomb on a black dot on a piece of white
paper, and examine with the "pile of plates" the two
dots produced. Remembering the plane of polarisation of the transmitted
light, see whether your results agree with those obtained by
the last method.
-
- (c) Place a second rhomb over the first, and draw
diagrams of the appearance of the dots at every rotation of 45°
of the upper rhomb. In particular explain the positions of the
two dots in each of the four positions in which only two
are left.
-
- (d) Test your explanation by examining these two dots
with the pile of plates.
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- ii. The optic Axis. - Place the piece of spar cut
at right angles to the optic axis, on a black dot or a pin-hole
in tinfoil, and see that it does not divide the light into two.
Test
 the light and see if it is polarised.
-
- iii. Nicols Prism. - (a) Place the nicol's prism
on the upper stage of the polariscope, and find the plane of
polarisation of the light it transmits. Is it along the line
AB?
-
- (b) See that two nicols produce more complete extinction
than can be got with the reflecting polariscope.
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- 355. Tourmalines. - Examine the pair of tourmalines.
Set them to allow the light to pass, and examine it with a nicol.
See that it is plane polarised. Note that the light they transmit
is coloured. (Hence for most purposes they are inferior to a
nicol.) See that they produce very complete extinction.
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TREATISE ON PRACTICAL LIGHT |
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- Colours of Thin Plates.
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- 356. Apparatus. - Polariscope; mica and selenite films;
double.image prism; Fox's wedge.
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- i. Mica and Selenite Plates. - (a) Set up the
polariscope with a nicol as analyser (i.e. in place of the pile
of plates or the mirror C),
 and arrange it
to extinguish the light. Also tilt the glass reflector, A, till
the extinction is as complete as possible.
-
- (b) Place a thin piece of mica or selenite
on the stage, and note that colour is produced.
-
- (c) Rotate the mica and see that in four positions
at right angles it has no effect. In each of these four positions,
rotate the nicol, and see that the effect is precisely the same
as if the mica were not present.
-
- (d) Place the nicol once more to extinction, and rotate
the mica - note that the colour is brightest at angles half-way
between the positions at which it has no effect.
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- (e) Leave the mica in the position in which it has
the greatest effect and rotate the nicol. Notice that when it
is turned 45° the mica once more has no effect; on rotating
another 45° the colour is again bright, but is the complementary
of what it was at first.
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- ii. Double Image Prism. - (a) Replace the nicol
by the double image prism and see that the separate half
images vary in the same way as those produced above, also that
they are always complementary, and therefore where they overlap
they form white. Note that the actual tint of the halves changes
suddenly to its complementary, and that till that change they
only vary by having more or less white mixed with them.
-
- (b) Replace the mica by other pieces and note that
the colour depends on the thickness.
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- iii. Fox wedge. - Place the Fox wedge on the stage
and note the colour changes. See that the colours pro-
- duced proceed as in Newton's rings, and that in this wedge
there are two orders of colour. (The wedges are made by cementing
equal thicknesses of mica together so as to form a flight of
steps each rising by an equal amount, see p. 461, Exercise
4....)
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- 357. In all the above cases plane polarised light falls on
the crystal (mica) and is, in general, at once split into two
beams, polarised in
 planes at right angles to one
another, which may, or may not be of equal intensity. These two
rays travel through the crystal with different velocities, and,
reaching the other side, have therefore gained or lost some fraction
of a wave-length on one another. Here they recombine.
-
- If either of the planes of polarisation of the light in the
crystal happens to coincide with the plane of polarisation of
the incident light, of course there will be only one ray
in the crystal. In this case, there can be no interference, whatever
the thickness of the crystal. Hence, in four positions at right
angles, the crystal has no effect as in Experiment 356, i. (c).
-
- If the plane of the incident light bisects the angle
between the planes of polarisation of the light in the crystal,
as in Fig. 374, the two rays will
- be of equal intensity. In
 this
case,
- the interference effects will be most marked; for should
one ray of any colour gain half a wavelength, that colour will
interfere completely.
-
- If one ray gains any whole number of wave-lengths of any
colour over the other ray, that colour will emerge in the same
relative phase as it entered, and will combine therefore into
a vibration in the same plane. So that, if the nicol is crossed,
that is, if it is arranged for extinction, that colour will remain
dark: or, if the field had been bright, that colour will remain
bright.
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TREATISE ON PRACTICAL LIGHT |
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- If one ray, gains an odd number of half wave-lengtlis over
the other for any colour, then suppose OA (Fig. 375) to be the
incident
 vibration; on entry it is resolved into
two components at right angles, OP and OQ. On emergence, if we
suppose one component vibration to be in the same phase as at
entry, to be, for instance, at Q' (Fig. 376), the other must
be in the opposite phase to the one at entry; it will thus be
at the other end of its swing at P'. The resultant of the component
displacements OQ' and OP' will be the displacement OB. Also,
as the component displacements at emergence will be along OQ'
and OP', and will be equal in amount to those at
incidence along OQ and OP the resultant displacement will be
always be along OB. That is, it is still plane polarised,
but in a different plane. If, in addition, the angle AOP (Fig.
375) is 45°, it will be polarised in a plane at right angles,
since the [angle] A'OB is double the [angle] A'OQ'. Therefore,
in a dark field, this colour (being rotated 90°) will appear
bright, and dark in a bright field. Thus, we
- see the colour depends on the thickness and why it changes
to its complementary on rotating the analyser through a right
angle.
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- If one ray gains 1/4 wave-length on the other for some colour,
then Q will be in the middle of its swing when P is at the end
of its swing, and vice versa. Hence, as they are at right
angles and of equal amplitude, the resultant will be a circular
vibration (Fig- 377). The colour will therefore appear equally
bright with all positions of the analyser. This is called circularly
polarised light. (This can only be true, of course, for one
colour at a time, and should be therefore
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- observed with a sodium flame. A film of mica of such a thickness
that it produces this effect is called a Quarter Wave Plate.
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- If the gain is no exact wavelength, 1/2 wave-length, or 1/4
 wave-length, the emergent light will have
an elliptic vibration, and will be called elliptically polarized
light. Such a colour will increase and fade as the nicol
is rotated, but in no position can it be completely extinguished.
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- If the gain were 1/4 wavelength, but the axes in the mica
were not at 45° with the plane of the incident light, the
amplitudes of the two rays OP, and OQ, would be unequal (Fig.
378). The effect would again be that the vibrations of the emergent
light would be elliptic and not circular.
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- 358. i. Norremberg Doubler. - Place the mica film
(Experiment 356, i.) on the mirror B. The colour will in general
be quite different. The light now has to pass twice through the
mica, and, therefore, as the ray which travelled most slowly
on going down will again travel most slowly after
reflection, it will lose twice as much as it would do were the
mica ol the stage D. The effect is thus the same as if a film
of double thickness had been placed on D.
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- This form of polariscope is often called
the Norremberg "doubler" in consequence of this action.
-
- ii. Quarter Wave Plate. - (a) Examine a quarter
wave plate of mica on the stage D (Fig. 365), using a sodium
flame. On rotating the analyser see that the intensity remains
unchanged. {The mica must have its axes at 45° with the plane
of polarisation.}
-
- (b) Place the quarter wave plate on B, and see that
it is bright in a dark field, and dark in a bright one, i.e.
it acts as a half wave plate.
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- iii. Half Wave Plate. - (a) Place a half wave plate
(i.e. a film of mica of a thikness that delays one component
of the light half a period) on D, and see that it behaves as
ii. (b).
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- (b) Place it on B and note the effects.
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- iv. Cause of Difference of Phase. - (a) Take
a small piece of mica of uniform thickness and scratch a line
on it parallel to the direction in which it has no effect, cut
it in two along some line
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TREATISE ON PRACTICAL LIGHT |
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- (such as the dotted one). Place the pieces on one another
with the scratch on each parallel and place it at 45° as
usual. Note the colour when on D (in white light). Now place
a single piece on B and see that you get the same colour.
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- (b) Take the same two pieces, but this time place
them so that the scratch on one is perpendicular to the scratch
on the other. Place the pair on either stage and see that it
has no effect on the light in any position. Explain this.
-
- To produce the Polarisation of Light with a Plate of Spar
cut normally to the Axis, using the difference between the Critical
Angles of the Ordinary and Extraordinary Rays.
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- 359. Apparatus. - A plate of Iceland spar cut perpendicular
to the axis as large and as thin as can be obtained; a glass
trough with parallel
- sides at sufficient distance apart to allow the spar to be
placed obliquely between them;l carbon bisulphide
or some alpha-mono-bromo-napthalene; a nicol or double-image
prism.
-
- Theory. - The refractive index of spar is given in
the following table:
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| Rays |
- Extraordinary
- Ray.
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- Ordinary
- Ray.
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A. |
1.4828 |
1.6501 |
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C. |
1.4847 |
1.6545 |
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D. |
1.4864 |
1.6585 |
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F. |
1.4908 |
1.6679 |
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G. |
1.4945 |
1.6762 |
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- l In place of the trough a glass
beaker, or better, a tube:with a plain glass bottom, may be set
up with its axis vertical, and the spar placed in this at the
angle of 20° with this veriical axis, and then the carbon
bisulphide poured in until its surface is above the spar; it
will be found that the light coming up vertically through the
spar is polarised.
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- The refractive index of alpha-mono-bromo-naphthalene at 20°
C, for the D line is 1.6582, which is almost identical with the
refractive index of the ordinary ray in spar. Thus the critical
angle for the ordinary ray is 90° and for the extraordinary
ray is about 64° (p. 28). The refractive index of carbon
bisulphide is 1.67, and the critical angles are 83° and 62°
respectively for yellow light.
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- Experiment. - If, therefore, the spar is placed in
the cell with its plane vertical, and making an angle of about
70° with the face of the trough, and if the trough is filled
with either of these liquids, the light from a distant source
falling upon the surface of the glass normally will enter
- the liquid, and when it reaches the surface of the spar the
extraordinary ray will strike the surface at an angle greater
than the critical angle, and therefore will be entirely reflected.
The ordinary ray will pass almost straight through it, as the
refractive index of the ordinary ray in the spar is nearly the
same as that in the liquid.
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- Examine each of the beams, the transmitted and reflected,
with a nicol, and see that they are polarised in planes perpendicular
to one another, the ordinary ray being polarised in the principal
plane, which is the plane of incidence, since the optic axis
coincides with the normal.
-
- Jamin suggested this arrangement as a polarising apparatus
(instead of the nicol's prism), but liquid prisms are awkward
to use. Feussner made one of glass and spar (Nature, March
27, 1884), but as he was unable to find a cement of sufficiently
high refractive index the prism was not very successful. The
reflected beam will only be perfectly polarised if the refractive
index is absolutely identical in the spar and the liquid.
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