P1. (a) If the eyeglasses have a positive lens, then the eye-lens
itself is too weak. The person has hyperopia.
(b) If the eyeglasses have a negative lens, then the
eye-lens itself is too strong. The person has myopia.
(c) If the eyeglasses are bifocals then the person
either has inadequate accommodation (presbyopia) or had cataract surgery
P2. (a) The near point is too far away. The
person has hyperopia.
(b) This is the normal situation – no
correction required.
(c) The near
point and far points are both too close. Mostly myopia – a single negative lens
almost fixes it.
(d) The main problem is presbyopia (inadequate
accommodation) – the near point and far point are almost the same value. The
solution would be bifocals, with a negative lens for distance and a positive
lens for close-up work.
P4. The student has astigmatism – the focal length of the eye is
different for objects whose axes are in different directions. Her glasses have
cylinder lenses whose variation in focal length compensates for the difference
in her eye lens.
P5. (a) To get the maximum magnification you would use the shortest
focal length, since the magnification is 25/f. This would be the f=2 cm lens.
(b) This lens would also have lots of aberrations and
distortions and a lens with a somewhat longer focal length would give a clearer
image, even though it would be smaller.
P6. (a) Use the shortest possible focal length for a magnifying
glass ignoring aberrations: f=25mm
would be the choice.
(b) A compound microscope uses two short focal length
lenses. f=25 mm for the objective and f=50
mm for the eyepiece.
(c) An astronomical telescope uses a long focal length for
the objective and a short one for the eyepiece. Objective f=200 mm,
eyepiece=25mm
(d) A Galilean telescope uses a long focal length for the
objective and a negative lens for the eyepiece. Objective=200 mm, eyepiece= -50
mm.