Download Optics 2 - University of Utah Physics

Optics 2: Spherical Lenses and Optical Instruments
Purpose of this Minilab
• Use lens formula to determine focal length of a lens.
• Learn about image magnification in magnifying
glasses, microscopes, and telescopes.
Optics 2: Spherical Lenses and Optical Instruments
Activity 1: Focal Length of a Lens
Method 1:
f
Flashlight or table lamp at the
end of classroom (long distance
compared to focal length).
Light rays enter lens
approximately parallel.
Lens
Screen or sheet of
paper to see image.
Move sheet until image is in focus.
Then measure f.
Optics 2: Spherical Lenses and Optical Instruments
Activity 1: Focal Length of a Lens
Method 2:
s
si
o
Object (illuminated cross
on the light source)
Screen or sheet of
paper to see image.
1 1 1
Move sheet until image is in focus.
 
Then measure so and si and calculate f with: f so si
Optics 2: Spherical Lenses and Optical Instruments
The Imaging Equation for Lenses
1
1
1


so
si
f
so: object distance
si: image distance
f : focal length
Optics 2: Spherical Lenses and Optical Instruments
Sign Rules For Lenses
Convex lenses:
Concave lenses:
f is positive
f is negative
Most objects are real.
Real objects:
Virtual objects:
so is positive
so is negative
Real images:
Virtual images:
si is positive
si is negative
Virtual images cannot be
picked up with a screen.
Optics 2: Spherical Lenses and Optical Instruments
Virtual or Real Image?
1 1 1
 
si f so
for positive f (convex lens) :
si  0 (real image) if so  f
si  0 (virtual image) if so  f
In Activity 1.2 (using a converging lens) place the object at a
distance larger than f away from the lens to get a real image.
Hint: To answer Q1, do a similar analysis for the concave lens (f < 0).
Optics 2: Spherical Lenses and Optical Instruments
Activity 2: Magnification
'
h image size
Magnificat ion : M  
h object size
An inverted image
means that h’and h have
opposite sign.  M < 0
h’
h
a
so
a
tan a 
si
h
so

h'
si
'
si
h

h
so
si
h'
M  
h
so
Optics 2: Spherical Lenses and Optical Instruments
2.2 Virtual image magnification (magnifying glass)
Without the magnifying glass:
eye
25 cm (typical nearest distance a human can focus on)
With the magnifying glass:
eye
f
virtual image
25cm
M
1
f
Optics 2: Spherical Lenses and Optical Instruments
Verifying this magnification of a magnifying glass
viewing screen
your
eye (close
to lens)
Optical Bench
linear graph
paper
 25 cm
lens
f = +100mm
hand held linear graph
paper (close to lens)
1)
2)
3)
4)
5)
6)
Tape linear graph paper on viewing screen.
Place lens about 25cm away from screen.
Hold a second piece of graph paper close to lens.
Move your eye close to the lens.
Move the second piece of graph paper so it is in focus.
Compare the size of graph paper seen through the lens
with the size of the graph paper on the screen (seen not
through the lens). See next page for illustration.
Optics 2: Spherical Lenses and Optical Instruments
What you should see ….
viewing screen
lens
Compare:
3.5 divisions
on the graph paper
taped to the screen
= 1 division on the
hand held graph
paper seen
through the lens.
hand held graph paper
seen through lens
hand held
graph paper
graph paper on
viewing screen
M=3.5
(in this example)
…then check whether this agrees withM 
25cm
1
f
Optics 2: Spherical Lenses and Optical Instruments
Remarks to formula for magnifying glass….
The actual magnification depends on exactly where the object is placed:
If the object you magnify is placed exactly at the focal point of the
magnifying glass, then you view with a relaxed eye and
25cm
M
f
If you move the object even closer to the lens, the magnification can get
as high as
25cm
M
1
f
 You could get a theoretical value anywhere between those two
magnifications, depending on where exactly you hold the paper.
Optics 2: Spherical Lenses and Optical Instruments
Activity 3: Microscope
virtual image
eye
so
si
eyepiece
fe=100mm
Me 
25cm
1
f
M  M oM e 
objective
fo=200mm
s
Mo  i
so
si  25cm 

 1
so  f

need so > fo
real image
between lenses
Optics 2: Spherical Lenses and Optical Instruments
Microscope: Building Instructions
Step 1: Install light source and objective lens.
illuminated arrow
on this side
200mm lens
(objective)
light source
handheld piece of paper:
move so that the image
of the arrow is in focus.
optical bench
so  30cm
measure si
record so and si
Optics 2: Spherical Lenses and Optical Instruments
Microscope: Building Instructions
Step 2: Install eyepiece lens.
100mm lens
(eyepiece)
200mm lens
(objective)
optical bench
so  30cm
Si
(as previously
determined)
some small
distance further
Optics 2: Spherical Lenses and Optical Instruments
Microscope: Building Instructions
Step 3: Replace light source with white viewing screen
linear graph
white
paper
viewing
200mm lens
screen
(objective)
100mm lens
(eyepiece)
optical bench
so  30cm
Si
Viewing screen must be placed where the arrow used to be.
Cover the viewing screen with linear graph paper.
Optics 2: Spherical Lenses and Optical Instruments
Microscope: Building Instructions
Step 3: Look through eyepiece and adjust it’s position.
linear graph
white
paper
viewing
200mm lens
screen
(objective)
100mm lens
(eyepiece)
eye
optical bench
so  30cm
Si
Adjust eyepiece position
so that the image of the
graph paper is in focus.
Optics 2: Spherical Lenses and Optical Instruments
Microscope: Measuring the magnification
linear graph
paper
200mm lens
(objective)
hand held
linear graph
paper
100mm lens
(eyepiece)
eye
optical bench
25cm
Step 1: Hold a second piece of graph paper approximately 25cm from your eye.
That extra graph paper should be a bit to the side so you can still see the image
of the graph paper that is on the viewing screen.
Optics 2: Spherical Lenses and Optical Instruments
Step 2: What you should see ….and measure
viewing screen
hand held
graph paper
(25cm from
eye)
image of graph paper
on viewing screen
Compare:
2.8 divisions
on the hand held graph paper
= 1 division on the image of
Graph paper taped to the screen.
M=2.8
(in this example)
graph paper on
viewing screen
…then check whether this agrees with
M
si  25cm 

 1
so  f

Optics 2: Spherical Lenses and Optical Instruments
Activity 3: Telescope
 fo + fe
virtual image
eye
si  fo
 fe
eyepiece
fe=100mm
so   (looking at far away objects)
objective
fo=350mm
M 
fo
fe
Optics 2: Spherical Lenses and Optical Instruments
Telescope: Building Instructions
Install objective and eyepiece
350mm lens
(objective)
100mm lens
(eyepiece)
optical bench
Separate objective and eyepiece
by fo+fe (=450mm)
Optics 2: Spherical Lenses and Optical Instruments
Telescope: Measuring the
Magnification
lamp
350mm lens 100mm lens
(eyepiece)
(objective)
eye
optical bench
View white board through
telescope from the back of
the room.
White board in the front of the room.
Draw a thick scale on the white board.
Illuminate the scale with a lamp.
Optics 2: Spherical Lenses and Optical Instruments
What you should see …
white board
telescope eyepiece
Compare scale seen through
telescope with scale seen
directly to determine M.
Here: Magnification looks like M  - 2.3 (negative because
inverted)
Optics 2: Spherical Lenses and Optical Instruments
Using the Desk Lamp
Lamp Plug (black) must be plugged
into dimmer plug.
Dimmer plug (white) must be plugged
into power outlet.
Dimmer
On/Off
switch
of lamp