Page 136 - July-August 2020

δi´ 1, (angle DB´ 1H) is also equal to
FIGURE 5. DERIVATION OF
THE EXPRESSION FOR PRISM angle δi2, the difference between
MAGNIFICATION the angles of incidence at the
second face.

Finally the rays are refracted
at the second face of the prism
whereupon they meet at B´ 2, where
the eye viewing through the prism is
situated. If the prism was not there,
the angle subtended at the eye by the
incoming rays would be angle δi 1. The
action of the prism is to alter this to
angle δi´ 2. The magnification which
is produced by the prism is the ratio
δi´ 2 / δi 1.

These angles can be found by
differentiating Snell’s law, to obtain

n cos i δi = n´ cos i´ δi´

and applying this to each surface
of the prism in turn, denoting the
refractive index of the prism material
by n, and remembering that the prism
FIGURE 6. TILT OF A PLANO-PRISM TO SHOW PRISM MAGNIFICATION. is surrounded by air, we find
VIEWED IN SIDE ELEVATION THESE FIGURES REPRESENT CHANGES IN PANTOSCOPIC
ANGLE FOR A BASE DOWN PRISM. VIEWED IN PLAN ELEVATION THE FIGURES REPRESENT δi´ 1 / δi 1 = cos i 1 / n cos i´ 1
CHANGES IN FACE FORM ANGLE FOR A BASE OUT PRISM BEFORE THE L EYE OR A BASE IN
PRISM FOR THE R EYE and δi´ 2 / δi 2 = n cos i 2 / cos i´ 2
and since, δi 2 equals δi´ 1 we obtain

δi´ 2 / δi 1 = cos i 1 cos i 2 / cos i´ 1 cos i´ 2
Producing plano prisms in is positioned.
curved form reduces the distortion The angles i 1, i´1, i 2 and i´ 2 are
slightly since the deviation at each The upper ray, QD, of the found from a ray trace through the
surface is also reduced, but it does incoming narrow fan meets the first prism and it is assumed that before
not remove the distortion. Needless surface of the prism at D, making
to say, subjects must learn to adapt an angle of incidence of i1 with the EVEN IN
to these changes in the shapes of normal to the surface. The lower ray, MONOCHROMATIC
objects when they are prescribed GH meets the surface at H making a LIGHT, A PRISM
strong prisms. slightly larger angle of incidence, i 1 +
δi 1, with the normal to the surface at EXHIBITS IMAGE
An expression for prism H. The angle, DB1H, between the DEFECTS WHICH
magnification can be derived from rays is δi 1. CAUSE ALTERATIONS
Figure 5 which shows the passage TO THE SHAPE OF
of a narrow fan of rays through a The rays are refracted at the
flat plano prism which is initially first face of the prism, the angles of IMAGES VIEWED
converging towards the point, B1, refraction being i´ 1 at D and i´ 1 + δi´ 1 at THROUGH THE
and after refraction by the prism H, when they converge towards B´ 1. PRISMS
meet at B´ 2 at which point the eye The difference between these angles,

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