'lass jBlocfts In iRefractfon 359

THE USE OF GLASS BLOCKS IN REFRACTION.

BY HENRY GARRETT,England.

Early in a school course on Light it is usual to introduce anexperiment with pins and glass blocks, in order to determine the"index of refraction." The customary method is open to theobjection that it assumes, on the part of the teacher, a knowledgeof the result to be arrived at, and is, in consequence, purely a veri-fication of a known law. But the experiment may be more broadlytreated and utilized to lead, on inductive principles, not only to theexistence of an "index of refraction," but also to the examinationof the limiting case.

In the first place, pupils will be set to find the paths of severalrays, of varying obliquity, passing through the glass. It is atonce apparent that the amount of bend increases as the incidentrays become more inclined to the normal. A ray striking nor-mally will also be found to be undeviated. It now becomes neces-sary to examine carefully what connection exists between thedirections of the incident and refracted rays. To do this the in-clination of each ray must in some way be measured. The usual

360 School Science an& /l&atbematfcs

method of expressing an incline, such as may be found on everyrailway, is to describe it as a rise of 1 in 100, 2 in 225, etc. Incase the ray falls normally on the glass surface, the incline iszero. For any other direction the incline is measured Lj draw-ing a perpendicular from any point, on the direction of the inci-dent ray, to the normal, e.g., if NO (Fig. 1.) be the normal to theglass surface, AO the direction of an incident ray, AN the per-pendicular drawn from any point A in AO to NO, then the in-

ANdine will in this case be ��. In the same way the incline of

AOBP

the refracted ray OB will be ��, where BP is the perpendicularBO

from any point B, in the direction of the refracted ray, to the

0-3

0.^

04

33-p

-BO.

O.Si

^0 C.SL ^ 0.^ O.S /�

A^L>/\Q ^FIG. 2

^ ^ ^ ^ ^ ^^ ^

^^ ^ ^

^ ^^^ ^ ^ ^

x^r^

<^’

normal. When these relations have been determined for eachpair of incident and refracted rays, the next course will be toobtain a graphical picture of the connection between them. Inan actual experiment carried out by a boy with crown glass, thefollowing ratios were obtained:

'lass 3Blocfts in 1Refractfon 361

’ Taking now the incline of the inci-� AN

dent ray, ��, as abscissa, and that of AN BP^ AO AOBOBP

the refracted ray, ��, as ordinate, the o’oo 0*00

BO 0-25 o’i6accompanying curve (Fig. 2) is obtained. 0*45 o’26As will be seen, it closely approximates °/2 ° .^’to a straight line, one point only beingappreciably out.

The meaning of the curve will be clear to any pupil who hasworked through a satisfactory preliminary course in physics, andhe should be able to write it down as

AN BP��=k, ��

AO BOwhere k is a constant. If the term sine is not yet known to thepupil, he may now be given the name, since he will understandwhat it indicates, and the equation becomes:

Sin i == k Sin r,or

Sin i____�� L-�����

�� K,

Sin rwhere i and r are the angles of incidence and refraction respec-tively.

The above evidently amounts to a rediscovery of Snell’s lawin the case of glass. The numerical value of k�the index ofrefraction�may either be taken from the curve, or calculatedfrom each pair of ratios in the table.

Pushing the consideration of the curve further, it will occurto the teacher to ask what is the greatest value that Sin i orAN �

�

�� can have. It will evidently be when the perpendicular ANAO

ANand the hypoteneuse AO become identical, or �� == 1, that

AOis, when the incident ray is parallel to the glass surface GO.Assuming that the above law holds for all possible values of

BPsin i, the maximum value of sin r or �� can be read off from

BO

362 School Science an& /l&atbematfcs

the curve. In the case before us it is 0.64. The angle correspond-’1ing" to this, as taken from a table of sines, is 39° 48’.

If now the ray be considered as reversed in direction, pro-ceeding outwards from the interior of the glass, the physicalinterpretation of the result will be that a ray striking the innersurface of the glass at an angle of 39° 48" with the normal willtravel along the surface of the glass, whereas any ray making asmaller angle than this will emerge. In other words, 39° 48’ isthe "critical angle" for glass. Looked at somewhat differently,the result given by the equation

Sin i == k Sin r,in the special case where sin i = 1, is

i

Sin R == �,k

where R is the "critical angle."�School World.

THE VALUE OF VACCINATION.

BY WILFRED H. MANWARING.Department of Pathology and Bacteriology, University of

Chicago."Do you advocate or oppose vaccination? And, why?"Few teachers who are asked these questions can cite authentic

facts in support of their belief. A brief summary of facts broughtout by governmental inquiry into the results of vaccination,might therefore be of value.

Historical: Vaccination was introduced in England in 1798,Its introduction was preceded by twenty-four years of observa-tion and experiment that lead Jenner to believe that the inocula-tion of a human being with cow-pox, a disease of cattle resem-bling mild smallpox, renders that person incapable of takingsmallpox. He inoculated a number of people with this cow-pox.and afterwards tried to infect them with real smallpox. The re-sults of his experiments were such that he announced cow-pox in-oculation, or vaccination, as a preventive of the graver disease.

This belief was subjected to experimental inquiry by a numberof physicians, and Jenner’s results confirmed by them. Thepractice of vaccination, therefore, rapidly gained favor in Eng-land. and was soon extended to other countries.