Irodov – Problems in General Physics

5.47. F < D/do = 20.

5.48. F= 60.

5.49. (a) F = 2a/o/do = 15, where /^0 is the distance of the best

vision (25 cm); (b) r < 2a/o/do.

5.50. The principal planes coincide with the centre of the lens.
The focal lengths in air and water: f = —110 = —11 cm, f'
= noleo = +15 cm. Here cl) = (2n — no — 1)1 R, where n and no^
are the refractive indices of glass and water. The nodal points coincide
and are located in water at the distance x = f' f = 3.7 cm from
the lens.
5.51. See Fig. 39.
5.54. (a) The optical power of the system is cb =cD 2 -

• d(1)0^2 = + 4 D, the focal length is^25 cm. Both principal planes

H H'

(a)

H' H

F

Fig. 39.

(c)

are located in front of the converging lens: the front one at a distance

of 10 cm from the converging lens, and the rear one at a distance of

10 cm from the diverging lens (x = d(1) 2 /0 and x' = — dcloin);

(b) d = 5 cm; about 4/3.

5.55. The optical power of the given lens is cD = clpi + cD^2 -

• (dln) c130 2 , x = d0 2 1 = 5.0 cm, x' —40^1 1 nal = 2.5 cm,
  i.e. both principal planes are located outside the lens from the side
  of its convex surface.
  5.56. f = tl tz. The lens should be positioned in the front
  fly- d
  principal plane of the system, i.e. at a distance of x =
  = -1- f^2 — d) from the first lens.
  5.57.^4 :13 = 2c13' — 20'^2 //no = 3.0 D, where cD' = (2n —no —1)/R,
  n and no are the refractive indices of glass and water.
  5.58. (a) d = nARI (n — 1) = 4.5 cm; (b) d = 3.0 cm.
  5.59. (a) cD = d (n-1) 2 1nR > 2 0, the principal planes are locat-
  ed on the side of the convex surface at a distance of d from each
  other, with the front principal plane being removed from the convex
  surface of the lens by a distance of RI (n — 1); (b) cb = (1/R 2 -1/R 1 ) X
  X (n — 1)/n < 0; both principal planes pass through the common
  curvature centre of the surfaces of the lens.

5.60. d = 1 / 2 n (R 1 R 2 )I (n — 1) = 9.0 cm, F = R 1 /R = 2 5.0.

5.61. (1) = 2(n 2 — 1)/n 2 R = 37 D.

5.63. p = 3.10 7 m; Oni= 1.6-10 m- 1.

5.65. 1.9a.

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