Fig. 5.6.5.26. By means of plotting find:
(a) the path of a light ray after reflection from a concave and
convex spherical mirrors (see Fig. 5.4, where F is the focal point,
00' is the optical axis);(a) (6)Fig. 5.4.(b) the positions of the mirror and its focal point in the cases
illustrated in Fig. 5.5, where P and P' are the conjugate points.
•pr •p(^0) O f 0
.p
(a) (^) (b)
Fig. 5.5.
5.27. Determine the focal length of a concave mirror if:
(a) with the distance between an object and its image being equal
to 1 = 15 cm, the transverse magnification 6 = —2.0;
(b) in a certain position of the object the transverse magnification
is Ni = —0.50 and in another position displaced with respect to the
former by a distance 1 = 5.0 cm the transverse magnification 6 2 =
= —0.25.
5.28. A point source with luminous intensity / 0 = 100 cd is
positioned at a distance s = 20.0 cm from the crest of a concave
mirror with focal length f = 25.0 cm. Find
the luminous intensity of the reflected ray
if the reflection coefficient of the mirror is
p = 0.80.
5.29. Proceeding from Fermat's principle
derive the refraction formula for paraxial
rays on a spherical boundary surface of ra-
dius R between media with refractive in-
dices n and n'.
5.30. A parallel beam of light falls from
vacuum on a surface enclosing a medium
with refractive index n (Fig. 5.6). Find the shape of that surface,
x (r), if the beam is brought into focus at the point F at a distance f
from the crest 0. What is the maximum radius of a beam that can
still be focussed?
P'.
0'