CHAP. 38]
38.9
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THIN LENSES
A lens has a convex surface of radius 20 cm and a concave surface of radius 40 cm and is made of glass of refractive index 1.54. Compute the focal length of the lens, and state whether it is a converging or a diverging lens. First, notice that r1 > 0 and r2 > 0 because both surfaces have their centers of curvature to the right. Consequently, 1 1 1 1 1 0:54 n 1 or f 74 cm 1:54 1 f r1 r2 20 cm 40 cm 40 cm Since f turns out to be positive, the lens is converging.
38.10 A double convex lens has faces of radii 18 and 20 cm. When an object is 24 cm from the lens, a real image is formed 32 cm from the lens. Determine (a) the focal length of the lens and (b) the refractive index of the lens material. 1 1 1 1 1 7 f so si 24 cm 32 cm 96 cm 1 1 1 1 n 1 n or f r1 r2 13:7
a b
96 cm 13:7 cm 14 cm 7 1 1 1 or n 1:7 18 cm 20 cm
or
f
38.11 A glass lens n 1:50 has a focal length of 10 cm in air. Compute its focal length in water n 1:33 . Using 1 f we get
1 r2 1 1 1 1:50 1 10 r r2 1 1 1:50 1 1 1 f 1:33 r1 r2
For air : For water :
n1 n2
1 1 r1
Divide one equation by the other to obtain f 5:0=0:128 39 cm:
38.12 Each face of a double convex lens has a radius of 20.0 cm. The index of refraction of the glass is 1.50. Compute the focal length of this lens (a) in air and (b) when it is immersed in carbon disul®de n 1:63 : We use 1 f a b
1 1:50 f 1 1:50 f 1:63
n1 n2
1 20 cm 1 1 20 cm
1
1 1 r1 1 20 cm 1 20 cm
1 r2
or or
f 20:0 cm f
125 cm
Here, the focal length is negative and so the lens is a diverging lens.
38.13 Two thin lenses, of focal lengths 9:0 and length of the combination.
6:0 cm, are placed in contact. Calculate the focal