1. 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.

2. Thin Lens + - Fo Fi f xo so si xi yo yi Quantity Sign so Real object
Virtual object si
Real image
Virtual image f
Converging lens
Diverging lens yo
Erect object
Inverted object yi
Erect image
Inverted image

3. IV.A Imaging by a single lens
Screen
Lens
Screen
Figure out the exact position of the filament!

4. Depth of field in photograph:
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.

5. Screen placed away from image plane: Blurry imageyo Fo Fi yi xo f f xi so si
Screen placed away from image plane: Blurry image

6. Screen placed away from image plane but using an aperture….. Apertureyo Fo Fi yi xo f f xi so si
Screen placed away from image plane but using an aperture…..
Aperture

7. 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
Mirror

8. IV.D Spherical aberration

9. 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 6 2 5 3 4 4 5 3 6 2 1
Perfect Lens

10. IV.D Foucault knife test explained
Foucault “knife” at position 1 (in front of focus)
Screen 1 6 2 5 3 4 4 5 3 6 2 1
Perfect Lens
Screen

11. IV.D Foucault knife test explained
Foucault “knife” at position 2 (at focus)
Screen 1 6 2 5 3 4 4 5 3 6 2 1
Perfect Lens
Screen

12. IV.D Foucault knife test explained
Foucault “knife” at position 3 (behind the focus)
Screen 1 6 2 5 3 4 4 5 3 6 2 1
Perfect Lens
Screen

13. 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 5 2 4 3 6 4 5 1 6 3 2
Lens with spherical aberration

14. 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

15. 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

16. 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!

17. IV.D Setting up your Foucault knife test
18mm lens
Razor blade
Screen
Light Source
Short ends towards each other
Razor blade
View from the front

18. IV.E Total internal reflection

19. IV.E Determine the refractive index of prism by measuring the critical angle

20. IV.E Determine the refractive index of prism by measuring the critical angle
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.

21. IV.E Careful when deriving nprism (Qcritical): There are two possibilities requiring you to count the critical angle positive or negative
Case A
Case B

22. IV.E The result will be (please derive):

23. 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

24. 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

25. IV.E Measuring the index of refraction of a liquid using two prisms
Before adding the liquid

26. IV.E Measuring the index of refraction of a liquid using two prisms
After adding the liquid

27. 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 a using Snell’s law.
Calculate d from trigonometric relationship.
Calculate nliquid from nprism and d using Snell’s law.

28. IV.E Beam expansion/contraction using a Kepler style telescope
Parallel Light:
Diameter Dout
Parallel Light:
Diameter Din
Eyepiece Lens
Objective Lens
How are Dout , Din , fo , and fe related? Use trigonometry!

29. IV.E Beam expansion/contraction using a Galileo style telescope
Parallel Light:
Diameter Din
Parallel Light:
Diameter Dout
Eyepiece Lens
Objective Lens

30. 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