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

Solutions
301

4.10. Let the spider be at point A (Fig. 236)

located above the upper point D of the sphere.

The spherical surface corresponding to the arc BDB'

of the circle is visible to the spider. Points B

Fig. 236

and B' are the points of intersection of tangents
drawn from point A to the surface of the sphere.
The ray AB propagates within the sphere along BC.
The angle cc can be found from the condition
1
sin a=
ng 1

where no is the refractive index of glass. This ray

will emerge from the sphere along CA' Therefore,

the fraction of the spherical surface corresponding

to the arc CD' C' will also be visible (by way of