Page 412 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 32] LENSES 397

SOLVED PROBLEM 32.2
A meniscus lens has one concave and one convex surface. The concave surface of a particular meniscus
lens has a radius of curvature of 30 cm, and its convex surface has a radius of curvature of 50 cm. The
index of refraction of the glass used is 1.50. (a) Find the focal length of the lens. (b) Is it a converging
lens or a diverging lens?
(a) Here R 1 =−30 cm (since the first surface is concave, its radius is considered negative), and R 2 =+50 cm.
Hence
1 1 1 1 1 −1
= (n − 1) + = (1.50 − 1.00) − + =−0.00667 cm
f R 1 R 2 30 cm 50 cm
1
f =− =−150 cm
0.00667 cm −1
(b) A negative focal length signifies a diverging lens.

SOLVED PROBLEM 32.3
A lens made of glass whose index of refraction is 1.60 has a focal length of +20 cm in air. Find its focal
length in water, whose index of refraction is 1.33.
Let f be the focal length of the lens in air and f be its focal length in water. The index of refraction of the

glass relative to air is n = 1.60 since the index of refraction of air is very nearly equal to 1. The index of refraction
of the glass relative to water is
index of refraction of glass 1.60

n = = = 1.20
index of refraction of water 1.33
From the lensmaker’s equation, since R 1 and R 2 are the same in both air and water,
f n − 1 1.60 − 1.00
= = = 3
f n − 1 1.20 − 1.00

and so f = 3 f = (3)(+20 cm) =+60 cm

The focal length of any lens made of this glass is three times longer in water than in air.

SOLVED PROBLEM 32.4
Both surfaces of a double-concave lens whose focal length is −9 cm/cm have a radii of 10 in. Find the
index of refraction of the glass.
From the lensmaker’s equation
1 1
n − 1 = = = 0.56
f (1/R 1 + 1/R 2 ) (−9cm)[1/(−10 cm) + 1/(−10 cm)]
n = 0.56 + 1 = 1.56

SOLVED PROBLEM 32.5

The focal length f of a combination of two thin lenses in contact whose individual focal lengths are f 1
and f 2 is given by
1 1 1
= +
f f 1 f 2
Use this formula to find the focal length of a combination of a converging lens of f =+10 cm and a
diverging lens of f =−20 cm that are in contact.