Irodov – Problems in General Physics

5.55. Calculate the positions of the principal planes and focal

points of a thick convex-concave glass lens if the curvature radius

of the_ convex surface is equal to Ri = 10.0 cm and of the concave

surface to R2 = 5.0 cm and the lens thickness is d = 3.0 cm.

5.56. An aligned optical system consists of two thin lenses with

focal lengths fl and 12 , the distance between the lenses being equal

to d. The given system has to be replaced by one thin lens which,

at any position of an object, would provide the same transverse

magnification as the system. What must the focal length of this lens

be equal to and in what position must it be placed with respect

to the two-lens system?

5.57. A system consists of a thin symmetrical converging glass

lens with the curvature radius of its surfaces R = 38 cm and a plane

mirror oriented at right angles to the optical axis of the lens. The

distance between the lens and the mirror is 1 = 12 cm. What is

the optical power of this system when the space between the lens

and the mirror is filled up with water?

5.58. At what thickness will a thick convex-concave glass lens

in air

(a) serve as a telescope provided the curvature radius of its convex

surface is AR = 1.5 cm greater than that of its concave surface?

(b) have the optical power equal to —1.0 D if the curvature

radii of its convex and concave surfaces are equal to 10.0 and 7.5 cm

respectively?

5.59. Find the positions of the principal planes, the focal length

and the sign of the optical power of a thick convex-concave glass

lens

(a) whose thickness is equal to d and curvature radii of the surfaces

are the same and equal to R;

(b) whose refractive surfaces are concentric and have the curva-

ture radii R 1 and R, (R,> Ri).

5.60. A telescope system consists of two glass balls with radii

R i = 5.0 cm and R^2 = 1.0 cm. What are the distance between the

centres of the balls and the magnification of the system if the bigger

ball serves as an objective?

5.61. Two identical thick symmetrical biconvex lenses are put

close together. The thickness of each lens equals the curvature

radius of its surfaces, i.e. d = R = 3.0 cm. Find the optical power

of this system in air.

5.62. A ray of light propagating in an isotropic medium with

refractive index n varying gradually from point to point has a cur-

vature radius p determined by the formula

1 a „

P^ ON

kin nj

where the derivative is taken with respect to the principal normal

to the ray. Derive this formula, assuming that in such a medium

the law of refraction n sin 0 = const holds. Here 0 is the angle be-

tween the ray and the direction of the vector Vn at a given point.

14-9451

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