CHAPTER IX.

Refracting Plates and Refracting Prisms.

50. A Refracting Plate is a portion of a refracting medium bounded by two parallel plane surfaces, as a pane of glass.

Suppose a ray of light enters and emerges from a refracting plate. Then if we recollect the principle that light would exactly retrace its steps and that the sides of the plate are parallel, we see that its direction on emergence must be exactly parallel to its direction before entering the plate. If a ray passing through any number of plates placed in contact come to a plate composed of its original medium, its course in this plate will be parallel to its original course.

By means of this experimental fact and the principle quoted it can be proved that if

μ, = index of refraction from medium A into medium B,

sin 0

the reader can easily prove

for himself that if μ, μ, μ......μ be the indices of refraction

2

from A into B, B into C, C into D...... and if μ=index from A into the last, then

51. To find the geometrical focus of a pencil of rays refracted through a plate (index = μ).

Let AC and BD be the sides of the plate: let QRST be the course of a ray. After refraction into the glass at the first surface at R we have the rays diverging from a focus 91, Fig. 39.

where

B

R

Aq1 =μ. AQ......(i)

Art. 36 (ii). The rays now form a diverging pencil in the glass, from q, therefore after refraction out of the glass at S into the air, they diverge as if from a focus 4, where

Here we have assumed as usual, what is only approxi

mately true, that the rays come accurately from the Geometrical Focus.

52. It can be shewn that when a ray is refracted out of one medium into another, as the angle of incidence increases, so also does the Deviation. Art. 34. This principle, which admits of an easy Geometrical proof, will be of great use in our investigations into the properties of prisms.

A prism is a portion of any refracting medium, bounded by two plane surfaces inclined at any angle to one another. The inclination of these faces to one another is called the "Refractive Angle."

The line in which these faces meet is called the "edge" of the prism.

We will now prove that "A ray passing through a prism of a medium denser than the surrounding medium is always turned from the edge of the prism."

(i) Let PQRS (fig. 40, (i)), be a ray passing through a plate bounded by parallel sides TR, VQ, and let RS be its direction after emergence.

(ii) By turning RT round into the position RT', we make our plate into a prism whose edge is turned towards T'V. The angle which QR makes with the normal has now increased, therefore the deviation

has increased, i.e. the angle which RS makes with the normal has increased still more, and the ray therefore emerges as RS nearer to the thick end of the prism than PQ. If the deviation did not increase it would emerge just parallel to PQ, i.e. it would not be bent at all.

(iii) Next we can turn our plate into a prism with the thick end towards T and N. The angle which QR makes with the normal has now decreased, therefore the angle which the emergent ray makes with the normal has now decreased still more, therefore the ray comes out as RS" nearer again to the thick end.

Thus in every case the emergent ray is turned from the edge.

53. The result of the last Article enables us to prove that "A ray passing through a prism is always turned to the edge of the prism, when the medium of which the prism is composed is denser than the surrounding medium."

54. We will now find the value of the deviation of a ray after refraction through a prism.

Fig. 41 (i).

A

M

(i) Let PQRS be the course of a ray: let the original and new directions of the ray meet in S.

Then

Deviation = RŜQ=RỘP – SRQ = RQA + 90°

−PQM− (90 − ŜRN+ A+ RQA)

=

- TRN- PÔM- A

=

= angle of emergence - angle of incidence - refractive angle of prism for rays above the normal.

(ii) Deviation=TSV=180~ RSQ=180 – TÊQ + SQR = 180-90+ TRN-A-RQA+ (RQA-90+ PQM) =TRN+PQM-A

for

= angle of incidence + angle of emergence-angle of prism rays below the normal.

55. Now it can be proved that when a ray makes the angle of emergence equal to the angle of incidence, the deviation is less than for any other ray.

=

If then D deviation, and be the angles of incidence and emergence, and A the refractive angle of the prism,