Modern Optics Lab Lab 4: First Experiments with the Advanced Optics Set Imaging with a single lens Aperture and its effect on depth of field Measuring.

Modern Optics LabLab 4: First Experiments with the Advanced Optics Set

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.

Topics


Quantity Sign

+ -so Real object Virtual objectsi Real image Virtual imagef Converging lens Diverging lensyo Erect object Inverted objectyi Erect image Inverted image

Fo Fi

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Thin Lens

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:formula Lens

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IV.A Imaging by a single lens

Lens Screen

os is

Lens Screen

os is

Figure out the exact position of the filament!


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.


Screen placed away from image plane: Blurry image

Fo Fi

fxo

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Screen placed away from image plane but using an aperture…..

Fo Fi

fxo

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Aperture


IV.C Auto-collimation method

Lens Mirror

f

Aperture

Make sure the image appearing here is a sharp image of the aperture, NOT an image of the filament!


IV.D Spherical aberration


IV.D Foucault knife test explainedNote: 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.

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Perfect Lens


IV.D Foucault knife test explainedFoucault “knife” at position 1 (in front of focus)

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Perfect Lens

Screen

Screen


IV.D Foucault knife test explainedFoucault “knife” at position 2 (at focus)

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Perfect Lens

Screen

Screen


IV.D Foucault knife test explainedFoucault “knife” at position 3 (behind the focus)

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Perfect Lens

Screen

Screen


IV.D Foucault knife test explainedIn 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)

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Lens with spherical aberration


IV.D Foucault knife test explained

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Foucault “knife” at position 1 (in front of “inner” focus)

Screen

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Foucault “knife” at position 2 (in front of “inner” focus)

Screen

Screen



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Foucault “knife” at position 3 (between “inner” and “outer” focus)

Screen

Screen This should be enough instruction for you to complete!


IV.D Setting up your Foucault knife test

Light Source

Short ends towards each other

18mm lens Razor bladeScreen

Razor blade

View from the front


IV.E Total internal reflection

critical1n

12 nn

1n

12 nn

criticalnnnn sin90sinsinsin :Law sSnell' 212211

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1sinn

ncritical


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

prismn1n

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

critical

prismn1n

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 critical.

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

critical

prismn

Case A

criticalprismn

Case B


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

A casefor 0 and

B casefor 0where2

critical

criticalcriticalprismn


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

Screen

Laser


IV.E Measuring the critical angle

Use the screen on the arm of the rotation stage to vie outgoing light ray.

Top view

Screen

Laser


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

criticalprismn

Before adding the liquid


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

criticalprismn

After adding the liquid


newcriticaprismn

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.

liquidn


IV.E Beam expansion/contraction using a Kepler style telescope

Objective LensEyepiece Lens

Parallel Light:Diameter Din

Parallel Light:Diameter Dout

How are Dout , Din , fo , and fe related? Use trigonometry!

ef of


IV.E Beam expansion/contraction using a Galileo style telescope

Objective LensEyepiece Lens

Parallel Light:Diameter Din

Parallel Light:Diameter Dout

of.)(negfe

eo ff


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

Modern Optics Lab Lab 4: First Experiments with the Advanced Optics Set Imaging with a single lens Aperture and its effect on depth of field Measuring.

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