W9_parallel_resonance.eps

Week 12: Lenses and Mirrors 395

• A telescope is used to view a distant object by making the angle its image subtends
  on the retina larger. Two lenses are situated at ends of a tube suchthat their focal
  points are coincident. The first lens (with a long focal length) formsareal image
  of the distant object more or less at its focal point. The second lens (with a short
  focal length) is used to view this real image as a simple magnifier. This produces a
  virtual image at infinity that subtends a greater angle than the original object did,
  viewable with the relaxed normal eye.
  The overall angular magnification of a telescope is given by:

M=−

fo

fe

(964)

The eyepiece lens can be converging (regular) or diverging (Galilean). In both cases

this formula for the magnification works (provided that one uses a negativefefor

the diverging lens and place the focal pointfoat the focal point on thefarside

of the diverging lens). A regular telescope inverts the image, which isinconvenient

and undesireable. A Galilean telescope does not invert the image.

• A compound microscope is used to view a very small, but nearby object. It ac-
  complishes this in two stages. Two short focal length lenses are situated at ends
  of a tube much longer tube. Thetube lengthℓof the microscope is by definition
  the distance between the focal point of the first, orobjectivelens (which must be
  converging) and the second, oreyepiecelens. The object is placed just outside of
  the focal length of the objective lens in such a way that it forms amagnified, real
  imageof the object more or less at the end of the tube length. The eyepiece lens
  is used as a simple magnifier to view this real image, and can be converging or
  diverging as was the case for the telescope. It produces a virtualimage at infinity
  that subtends a greater angle than the real image formed by the objective lens alone
  would if viewed at the near point of the relaxed normal eye.
  The magnification of the objective is:

Mo=−

ℓ

fo

(965)

The magnification of the eyepiece (simple magnifier) is:

Me=

xnp

fe

(966)

The overall magnification is therefore:

Mtot=−ℓ xnp

fofe

(967)

where as before, this formula for the magnification works providedthat one uses a

negativefefor the diverging lens and place the real image formed by the objective on

thefarside of the diverging lens. A regular microscope inverts the image, which is

inconvenient and undesireable. A “Galilean” microscope does not invert the image.

12.1: Vision and Plane Mirrors

Objects in the real world that are illuminated by diffuse light absorb the light at every

point on their surface and then reradiate (selected colors/frequencies) from each point

in all directions. This is why you can see something that is illuminated from all angles

• every point on its surface emits light reradiated from the illuminatingsource in all
  directions so no matter where you look at it from, some of the light reaches your eye.