Aptitude Test Problems in Physics Science for Everyone by S Krotov ( PDFDrive.com )

302 Aptitude Test Problems in Physics

an example, the optical path of the ray A KLM
is shown).
The surface of the spherical zone corresponding
to the arcs BC and B'C' will be invisible to the
spider.
The angle y is determined from the condition

cos

R

y=

R+h '

where R is the radius of the sphere, and h is the

altitude of the spider above the spherical surface.

Since R> h by hypothesis, y 0. We note now

that fl = n — 2a and sin a = 1lne I• Therefore,

0. 7t — 2 arcsin 1 ) —n
   ngi 2

Thus, the opposite half of the spherical surface is

visible to the spider, and the fly must be there.

4.11. None of the rays will emerge from the lateral

surface of the_cylinder if for a ray with an angle of

Fig. 237

Incidence y x n/2 (Fig. 237), the angle of incidence

a on the inner surface will satisfy the relation

sin a > 1/n. In this case, the ray will undergo

total internal reflection on the lateral surface.

It follows from geometrical considerations that

1

sin a= Yi —sins 0, sin 0.--.