II. New multiple-beam localised fringes formed by strongly curved silvered thin plates

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Submitted on 1 Jan 1950

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II. New multiple-beam localised fringes formed by

strongly curved silvered thin plates

S. Tolansky

To cite this version:

II. NEW MULTIPLE-BEAM LOCALISED FRINGES FORMED

BY STRONGLY CURVED SILVERED THIN PLATES

By S. TOLANSKY.

Sommaire. 2014 Si une feuille mince de mica doublement argentée est courbée suivant un cylindre de quelques centimètres de rayon et éclairée en lumière _{monochromatique parallèle,} il se forme un

système de franges rectilignes tres fines, localisées dans un _{plan passant par} le centre de courbure. Les

propriétés des _franges sont décrites. Il _apparaît d’intéressants effets de dédoublement par biréfringence. Les marches de clivage dans le mica sont révélées avec une haute _précision. On _peut utiliser la cryolithe

et d’autres couches pour produire le système. les variations dn système sont discutées.

LE JOURNAL DE PHYSIQUE ET LE RADIUM. TOME

_’11,

JUILLET

_1950,

PAGE 434.

Introduction. - In this section

an account is

given

of a new

_system

of

_fringes

which the writer has

developed.

The

_experiments

have been made witli the assistance of Mr N.

Barakat,

and a _very brief

preliminary descriptive

Note has

_already

_appeared

elsewhere

_(Nature,

_{T g48,}

162,

p.

8 I 6).

If a thin

Fig. 2.

flexible

_plate,

such as a sheet of

_mica,

or

celluloid,

or thin blown

_glass

is silvered on both sides and then bent

_{cylindrically}

into a curve

_(a

radius of cur-vature of 5 cm is a convenient

value,

but the

_precise

value is of no

_importance),

_very

_sharp

_strictly

localised

_fringes

can be

obtained,

either on a

_plane,

or on a _curve,

_according

to he directions of illu-mination and curvature.

Various modifications of the

_fringes

under dis-cussion have been obtained both in transmission

and in

reflection,

both with monochromatic and with white

_light,

with thick films and with thin

films,

with

_birefringent

and

_isotropic

films,

also with

_cylindrical

and with

_spherical

films. It is not the intention here to

_analyse

in detail the various

_complexities

met with and the

_simplest

case

_{only will}

be treated. The mode of formation

and the

_origin

of localisation are shown in the

simplified diagram figure

2, and which refers to a

thin

_cylindrical

_film,

illuminated with

_strictly

parallel

monochromatic

_{light (green}

_mercury)

produced by using

a

_point

source at the focus of a

good

lens. The surfaces of the curved film are

silvered

_(R

> go per

cent)

and as a result

multiple-beam interference takes

_place.

An incident ray

suffers

_multiple

reflections,

and

_provided

the film

thichness t is

_small,

all the beams

_effectively

unite at one

_point,

in accordance with

_{principles already}

developed (see

M. B.

_I.).

It is clear that with a

_cylindrical

_film,

a

_fringe

will form at the

_point

A. At the

_appropriate

position

B where the total

_path

difference alters

by

a

_wavelength,

another

_fringe

will form.

_By

means of a

_{simple geometrical}

_{construction,}

which

it is

_hardly

worth while

_giving

_here,

it can

_readily

be demonstrated that to a _{very close}

_{approximation}

fringes

will

_form,

localised on a

_{plane passing}

through

the centre of

curvature,

and if t is small

the surface of localisation deviates

only

very

slightly

from a true

_plane.

Experimental. -

The

_{fringes given by}

a flexed

piece

of muscovite mica are shown in

_plate

4.

They

can be seen on a screen

_placed

_passing

_through

the centre of

curvature,

or seen

_directly

with a

low power

microscope. They

exhibit certain

inte-resting

features,

as follows :

( 1 )

The

_fringes

are double. This is

_initially

due

to the

_{birefringence}

of the

mica,

for the dual

_fringes

are

_plane

_polarised

_mutually

_{perpendicularly.}

435

(2)

The

_fringes

are

_{highly sharply}

_localised,

but

only

if the mica is

_thin,

_preferably

less than

_{I / I o th rxlm .}

(3)

The

_fringes

have a

_highly

_sharpened

multiple-beam

intensity

distribution. This is

due,

not

_only

to the usual

_{multiple-beam}

_Airy

_{distribution,}

but is much enhanced

_by

the fact that the outer orders involve

_{quite high angles}

of

_incidence,

since incidences _range from normal to above 8oo. The effective

_reflecting

coefficient of the silver surface

is very

high

for the

_higher

_incidences,

with

conse-quent

increase in

_{fringe sharpness.}

(f~)

An

_approximate

calculation of the «

dia-meters )) of the

fringes

leads to an

_expression

of a form

_resembling

that of

_Fabry-Perot

_fringes.

A

calculation,

which is a close

_{approximation}

can be

made if

_dispersion

effects are

_neglected,

and errors

due to the

_large

_angles

involved are

_disregarded.

One then arrives at an

_expression

for diameter d

which is ’

in which R is the radius of

_{curvature, p}

the refractive

_{index, ~}

the

_wavelength

_{p the}

_fringe

order and E the fractional order at centre. This

closely

resembles the formula for

_Fabry-Perot

fringes.

When a

_spherical

film is

_used,

the

_fringes

seen

are

_circles,

not

_straight

lines. It is

_evidently

clear

from the

_geometry

that each

_fringe

arises from the

locus of

_points

at which the

_angles

of incidence of beams

_contributing

to _{any one}

_specific

_fringe,

make the same

_angle

with the

_tangent

to the curved surface.

Furthermore,

the

_fringe

_appearance and

fringe

formation can be

_regarded

as more or less

closely

related

_{(almost intermediate)}

to the classical

systems

of

Lummer,

now

_usually

called either

fringes

of

_equal

thickness or

_fringes

of

_equal

incli-nation. I _{therefore propose}

_naming

these new

fringes

as

_{" Fringes o f equal tangential}

inclination ".

The

_{birefringent fringe doubling.}

- The

fringe

doubling

is a

_complex

matter

_involving

two distinct features

_(a)

_{crystallographic, (b)’}

metal

_optics.

It will be noticed from

_plate

4

that the

_{fringe doubling,}

as a fraction of an

_order,

actually

increases on

_moving

away from the centre. It is thus not a

_simple

constant in terms of order

_separation.

It is found that with

_increasing

0 the

_fringe

_doubling

dimi-nishes and

_practically

ceases, but then

begins

once

Par. _4.

more. The

_explanation

is

_simple

when one recalls

, that

moving

across the

_fringe

_system

_corresponds

effectively

to a

_change

of incidence from

_-goo

to + goo.

Thus the

_{birefringence}

alters and one finds the

_optical

axes where the

_crystal

is

_effectively

no

_longer

_biaxial,

and at these sections the

_fringes

are

_single.

As to which

_{particular fringes}

become

_single

is

entirely dependent

on how the mica has been bent

relative to its own

_optic

axes.

Differential

_{phase change}

effect. -- It will

be noticed that as the incidence

increases,

two additional features affect the

_{fringe doubling (a)}

one of the

_fringe

_{pair sharpens,}

_(b)

it also weakens. It will be

_{immediately recognised}

that here we have

in

_reality

a _very

_complex

_situation,

for this is

_merely

a

_repetition

of the differential

_phase

_change

effect

already

described in

_Paper

II. It will be recalled that

_angles

of incidence are

_high.

Thus the observed

fringe separation

is a combined effect

_representing

the

_{birefringent displacement}

and added

numeri-cally

is the

_{phase change displacement.}

Now

the

latter,

having already

been

determined,

can

be

_deducted,

and the true

_{birefringence}

effect

obtained.

That this

_explanation

of the observed effect is indeed correct has been

_firmly

established

_by