The Optical Communications Reference

magnification V

1

, to the position 2 where again the sharp

image is observed on the same screen, but at magnifica-

tion V

2

¼1/V

1

. The distance between positions 1 and 2 is

a ¼ 45 mm. Find the focal length of the lens and estimate

the uncertainty of the measured value if the lens thick-

ness, t, is about 5–6 mm.

P.1.1.5. Location of the principal planes of a thick lens.

Find the positions of two principal planes H and H

0

, BFL,

and FFL of a lens made of glass BK-7(n ¼ 1.5163) having

two spherical surfaces of radii R

1

¼50 mm and R

2

¼

75 mm and thickness t ¼ 6 mm.

P.1.1.6. Violation of homocentricity of a beam passed

through a flat slab. A flat slab of glass is illuminated by

a homocentric beam which fills the solid angle u ¼1.5 sr

with the center at point A, 30 mm behind the slab

(Fig. 1.1.11). The thickness of the slab t ¼ 5 mm and

refractive index n ¼ 1.5. Find the location of the point A

0

after the slab as a function of incident angle, i, and esti-

mate the deviation of the outgoing beam from

homocentricity.

P.1.1.7. A two-lens system in the paraxial range. A lens

L

1

of 100 mm focal length is followed by a lens L

2

of

75 mm focal length located 30 mm behind it. Consid-

ering both lenses as a unified system find the equivalent

optical power and position of the focal plane.

P.1.1.8. A ball lens. Find the location of the principal

planes of a ball lens (a full sphere) of radius r ¼3 mm and

its BFL.

1.1.2. Thin lenses layout.

Microscope and telescope optical

configurations

We will consider here the following basic configurations:

(i) magnifier; (ii) microscope; and (iii) telescope. All

three can be ended either by a human eye or by an

electro-optical sensor (like a CCD or other area sensor).

1.1.2.1. The human eye

Although the details of physiological optics are beyond

the scope of this book, w e have to consider some im-

portant features of the human eye (for further details,

see Hopkins, 1962) as well as eye-related characteristics

of optical devices. Usually the ‘‘standard eye’’ (normal

eye of an adult person) is described in terms of a simpli-

fied model (so-called ‘‘reduced eye’’) as a single lens

surrounded by the air from the outside, and by the op-

tically transparent medium (vitreous humor) of re-

fractive index 1.336 from the inside. As a result, the

front focal length of the eye, f, differs from the back focal

length, f

0

(see Eq. (1.1.2)). The front focal length is

usually estimated as 17.1 mm where as f

0

is equal to

22.9 mm. The pupil of the eye varies from 2 mm (min-

imum size) to 8 mm (maximum size) according to the

scene illumination level (adaptation). The lens creates

images on the retina which consists of huge numbers of

photosensitive cells. The average size of the retina cells

dictates the angular resolution of the eye (ability of

seeing two small details of the object separately). The

limiting situation is that the images of two points are

created at two adjacent cells of the retina. This renders

the angular resolution of a normal eye to be 1 arcminute

(3  10

4

rad). The lens curvature is controlled by the

eye muscles in such a way that the best (sharp) image is

Fig. 1.1.9 Problem P.1.1.2 – Imaging by the graphical method:

(a) with a positive lens; (b) with a negative lens.

Fig. 1.1.10 Problem P.1.1.4 – Method of focal length

measurement.

Fig. 1.1.11 Problem P.1.1.6 – Consideration of a parallel plate.

7

Geometrical optics CHAPTER 1.1