Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
Topics
 Imaging with a single lens
 Aperture and its effect on depth of field
 Measuring the focal length with the “auto-collimation” method
 Spherical Aberration and the Foucault knife test
 Total internal reflection: Determining the index of refraction of a liquid
with “Abbes Method”.
 Building a beam expander.
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
Thin Lens
yo
Fo
Fi
yi
xo
f
so
Lensformula:
1 1 1
 
s0 si f
xi
f
si
T ransverseMagnification :
si
yi
MT 

so
yo
Quantity
so
si
f
yo
yi
Sign
+
-
Real object
Real image
Converging lens
Erect object
Erect image
Virtual object
Virtual image
Diverging lens
Inverted object
Inverted image
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.A Imaging by a single lens
Lens
so
Screen
si
Lens
so
Screen
si
Figure out the exact position of the filament!
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.B Depth of Field
Depth of field in photograph:
 The range of distances over which the image is sharp.
 Can be controlled with aperture.
 Depth of field is a trade-off for time of exposure in
photography:


Smaller aperture = greater depth of field but requires longer exposure
time.
Larger aperture = less depth of field but requires less exposure time.
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
yo
Fo
Fi
yi
xo
f
so
xi
f
si
Screen placed away
from image plane:
Blurry image
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
yo
Fo
Fi
yi
xo
f
so
Aperture
xi
f
si
Screen placed away
from image plane but
using an aperture…..
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.C Auto-collimation method
Make sure the image appearing here is a
sharp image of the aperture, NOT an
image of the filament!
Aperture
Lens
f
Mirror
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.D Spherical aberration
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.D Foucault knife test explained
Note: The different colors used are just for the purpose of easier visual tracking.
They do not represent different colors. Assume all rays have the same color.
1
2
3
6
5
4
4
5
6
3
2
1
Perfect Lens
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.D Foucault knife test explained
Foucault “knife” at position 1 (in front of focus)
Screen
1
2
3
6
5
4
4
5
6
3
2
1
Perfect Lens
Screen
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.D Foucault knife test explained
Foucault “knife” at position 2 (at focus)
Screen
1
2
3
6
5
4
4
5
6
3
2
1
Perfect Lens
Screen
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.D Foucault knife test explained
Foucault “knife” at position 3 (behind the focus)
Screen
1
2
3
6
5
4
4
5
6
3
2
1
Perfect Lens
Screen
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.D Foucault knife test explained
In this example of a lens with spherical aberration, we assume for simplicity two
different focal points: One for “outer rays” (1,6) and one for “inner rays” (2,3,4,5)
1
2
3
5
4
6
4
5
6
1
3
2
Lens with
spherical
aberration
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.D Foucault knife test explained
Foucault “knife” at position 1 (in front of “inner” focus)
Screen
1
2
3
4
5
6
Lens with
spherical
aberration
Screen
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.D Foucault knife test explained
Foucault “knife” at position 2 (in front of “inner” focus)
Screen
1
2
3
4
5
6
Lens with
spherical
aberration
Screen
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.D Foucault knife test explained
Foucault “knife” at position 3 (between “inner” and “outer” focus)
Screen
1
2
3
4
5
6
Lens with
spherical
aberration
Screen
This should be
enough instruction for
you to complete!
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.D Setting up your Foucault knife test
18mm lens
Razor blade
Light Source
Short ends towards each other
Razor blade
View from the front
Screen
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.E Total internal reflection
n2  n1
n1
n2  n1
n1
critical
Snell's Law : n1 sin 1  n2 sin 2  n1 sin 90  n2 sin critical
n1
 sin  critical 
n2
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.E Determine the refractive index of prism by measuring the critical angle

45 
n 1
n prism
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.E Determine the refractive index of prism by measuring the critical angle
critical
n 1
45 
n prism
Note: We call the angle on the left the “critical angle” here. That is a bit
different notation compared to the previous example of critical angle.
Task: Derive the relationship between nprism and Qcritical.
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.E Careful when deriving nprism (Qcritical): There are two possibilities requiring
you to count the critical angle positive or negative
critical


n prism
critical
n prism
Case A





Case B

Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.E The result will be (please derive):
n prism  2   critical where  critical  0 for case B
and
 critical  0 for case A
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.E Measuring the critical angle
 Use the angular translator and position prism such that the laser hits the prism exactly
at the rotational axis of the rotation stage.
 Reorient prism such that when the rotation stage is at 0 degrees the laser light is
back-reflected (make sure back-reflection goes back into laser).
 Use the screen on the arm of the rotation stage to vie outgoing light ray.
Top view
Laser
Screen
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.E Measuring the critical angle
 Use the screen on the arm of the rotation stage to vie outgoing light ray.
Top view
Laser
Screen
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.E Measuring the index of refraction of a liquid using two prisms
critical
n prism
Before adding the liquid
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.E Measuring the index of refraction of a liquid using two prisms
critical
n prism
After adding the liquid
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
nliquid
critica new





n prism
Reorient to find the new critical angle.
Determine nliquid from the new critical angle.
Do not assume that the critical angle is “small”.
Use numerical value of nprism from the previous result.
Derive in “steps”:
• Knowing nprism and the new critical angle, calculate  using Snell’s law.
• Calculate  from trigonometric relationship.
• Calculate nliquid from nprism and  using Snell’s law.
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.E Beam expansion/contraction using a Kepler
style telescope
fe
fo
Parallel Light:
Diameter Dout
Parallel Light:
Diameter Din
Eyepiece Lens
Objective Lens
How are Dout , Din , fo , and fe related? Use trigonometry!
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
IV.E Beam expansion/contraction using a Galileo
style telescope
f e (neg.)
fo
Parallel Light:
Diameter Din
Parallel Light:
Diameter Dout
Eyepiece Lens
fo  fe
Objective Lens
Modern Optics Lab
Lab 4: First Experiments with the Advanced Optics Set
Advanced Optics Set Components
 In the manual called “Advanced Optics Set” on page 3 there is a list of
components. Check to make sure all of them are in your set. Note that most sets
only have one prism. You will need to borrow a second prism from the TA as
needed.
 On page 4 of that manual at the bottom, there is a list of “offsets” for each
component. Example: Lenses have an offset of 6.5mm. Keep that in mind when
reading out the location using the marker on the component holder.
6.5 mm