Physics 2020
Prof. Steven Pollock
23-18
Summary of sign conventions:
Converging lens
Diverging lens
Real object
Real image
Virtual image
Upright image
Inverted image
f>0
f<0
do > 0
di > 0
di < 0
hi > 0
hi < 0
Example: Object inside of focus of converging lens
Image is virtual, upright, enlarged, inside focus:
So di = -3.3 cm
Negative = virtual, (less than 5 cm)
Physics 2020
Prof. Steven Pollock
23-19
If you want an object to look larger, you bring it closer. But you
can’t bring it closer than “N”
The max angle θ an object of height ho can “span” inside your eye
is thus tan θo (max)= ho/N
(tanθ ≅ θfor small θ)
What if θo (max) is still too small? Magnify θ with a lens!
Magnifying Glass (Giancoli 25-3) Same principle as example on
previous page: Usually put object at focus, so rays come out
parallel. Choose f < N ~ 25 cm for most people.
Object at focus =
rays come out
parallel.
Now, put eye right
in front of the
lens.
Parallel rays come into your eye = you see a pointlike object at
“infinity,” tipped up by angle θ` ~ho/f.
Angular Magnification
E.g:f (lens)=5cm, M=N/f~25cm/5cm=“5X”(5 times magnification)
Physics 2020
Prof. Steven Pollock
23-20
Telescopes (25-4 in Giancoli)
Sometimes 2 lens (or more) can be combined to produce useful
images. E.g. Astronomical refracting telescopes:
Big (large f) “objective lens”
Small (short f) “eyepiece lens”
Since do =
, objective lens produces a real “intermediate”
image at di = f objective. Then the eyepiece is f eyepiece behind
that = you get an image of that intermediate image! The eyepiece
is like a “magnifying lens” in the last example: With the
intermediate image at the focus, your (relaxed) eye sees the angle
of the image magnified (angular magnification).
Geometry:
[Image is inverted.]
= angular magnification