716
15 Optics
diagram. (You can assume that the chocolate does not melt because of the
microwaves.)
[University of Aberystwyth, Wales]
15.8 Each of the angles of a prism is 60 ◦ and the refraction index for sodium light
is 1.5. Sodium light is incident at the correct angle for minimum deviation.
Calculate the deviation of that portion of the light, which finally emerges from
the prism, after having suffered one internal reflection.
[University of Durham]
15.9 Write down the lens maker’s formula relating the focal length of a lens to the
object and image distances. Explain the sign convention used for the distances
involved.
Show that as two lenses are brought into contact, the focal length of the combined system, f , can be expressed as
1
f
=
1
f 1
+
1
f 2
where f 1 and f 2 are the focal lengths of the two separate lenses.
[University of Durham 2001]
15.10 An object is placed at a fixed distance D from the screen. Real images of the
object are formed on the screen for two positions of a lens, separated by a
distance d. Show that
(a) the ratio between the sizes of the two images will be
(D − d) 2
(D + d) 2
(b) The object size =
√
I 1 I 2 , where I 1 and I 2 are the sizes of the images
(c) f =
D 2 − d 2
4D
(d) D > 4 f
15.11 (a) Derive the lens maker’s formula
1
f
= (n − 1)
1
r 1
−
1
r 2
for a thin lens.
(b) A biconvex lens of plastic of refractive index n = 1.2 is immersed in
water (n = 1.33). Would the lens act as a converging lens or diverging
lens?
15.12 A combination of two thin convex lenses are placed as in Fig. 15.9. An object
is placed 5 cm in front of the first lens which has a focal length of 10 cm. The
second lens is 10 cm behind the first lens and has a focal length of 12 cm.