412 Week 12: Lenses and Mirrors
The magnification of the objective stage is:Mo=−ℓ
fo=−fo+l
s (1005)where the first relation is the one actually used, but the second one(based on the
observation thats′=fo+l) can be used to find the correct object distancesthat will
accomplish this.fo fo lαyy’s s’βfeFigure 176: The second magnification stage of a compound microscope brings thehighly magnified
image from the objective stage close to the eye by functioning as a simple magnifier. By bringing
the virtual image in fromxnptofeit magnifies it by an addtional factor ofxfnpe.
This real, magnified image can be viewed with the naked eye, but of course the naked
eye can view it nocloserthanxnp. The second stage of a compound microscope consists
of an eyepiece lens is used as asimple magnifierto view this real image in precisely the
same way we used it for the telescope, and can be converging or diverging as was the
case for the telescope. It produces a virtual image at infinity thatsubtends 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 eyepiece used as a simple magnifier is therefore:Me=xnp
fe (1006)
which yields an overall magnification for the two stages working together of:Mtot=−ℓ xnp
fofe(1007)
As we noted and can see in figure (177) above, one can use a diverging lens for the eyepiece
by placing the real image formed by the objective on thefarside of the diverging lens
to form a“Galilean” microscope. As before (for the telescope) this microscope does
not invert the image (inversion is inconvenient and undesireable) butotherwise the same
formula works for the magnification provided that one uses a negativefefor the diverging
lens. It has the further advantage of having a slightly shorter overall length.
Typical numbers for a compound microscope this might befo=fe= 1 cm,l= 10 cm, for
a total magnification of 250 (inverting or non-inverting). 250x microscopes aremore than