W9_parallel_resonance.eps

410 Week 12: Lenses and Mirrors

This image (virtual object) is “infinitely” smaller than the original object but it has the

advantage of beingright there in spacein front of the eye, not infinitely distant. We can

therefore examine it quite closely. To do so, we use a second lens as asimple magnifier,

placing it so that the virtual object is atitsfocal point. This is shown in the second

panel.

Since the virtual object is at the focal pointfe, rays diverging from the virtual object

exit the second lens parallel to the central ray, shown entering atangleβ. This bundle

of parallel rays corresponds to a virtual image at (negative) infinity but deflected so

that their angle relative to the central axis if much steeper. We caneasily compute the

angular magnification of this telescope by noting that:

α≈tan(α) =−y

fo

(1001)

and

β≈tan(β) =

y

fe

(1002)

so that

M=

β

α

=−

fo

fe

(1003)

In the final panel, we show what happens when this final image at infinity coming in

at angleβlooks like when closely viewed by a human eye. Since the image is infinitely

distant (the rays enter the eye parallel) it can be comfortably viewed with the relaxed

normal lens, which will focus the bundle down to a single point on the retina determined

by the central ray at angleβ. Obviously the total angle subtended on the retina is much

larger – the object being viewed appears much larger to the eye andsenses. The major

disadvantage of this telescope is that itinvertsthe image – everything viewed is upside

down and backwards. This makes it a bit tricky to find objects as they move theopposite

way one thinks that they should when viewing them through the telescope.

Interestingly, this final disadvantage can easily be eliminated by using adiverginglense

for the eyepiece. Ordinarily one thinks of a diverging lens as making something smaller,

but because we can place the image from the first lens anywhere we wish, we can turn

it into a virtual object at thefarfocal point of a diverging lens. One obtains the same

formula for the magnification, but nowfe<0 and the overall angular magnification is

positive.

α β

fe

y

fo

Figure 174: A “Galilean” telescope uses adiverginglens for the eyepiece. This does not affect the
formula for the magnification, but it ensures that the eye sees thedistant objectserectinstead of
inverted.

This kind of telescope is called aGalilean telescopeand is much more convenient to

look through than a regular telescope. As you can see from figure (174), the angular