Optics Lab

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Lab #1 Thin Lenses and Uncertainties in Measurement Worksheets

Please watch “Lab1 Lecture Part I” and “Lab1 Lecture Part II” in D2L before completing the worksheets.

Part A: Determine the focal length f of a converging lens

Technique 1: Using a lens-mirror combination

Instructions: View the 1st segment of the video, “CSEC Physics Virtual Lab (YouTube Video),” in D2L. Use the pause button when necessary so that you can read measurements. Do not use the measurements given by the video, as they do not give the correct number of significant figures and do not include uncertainties.

1) In the video, the smallest division of the tape measure is ________________ .

The uncertainty in measurements using this tape measure is _______________.

The focal length of the converging lens is found to be ___________________________. (Note: Make sure to include the correct number of significant digits in the reported value AND include the uncertainty in the stated result.)

2) Draw a ray diagram for the lens-mirror combination below. Show that when the object is of a focal length away from the lens, an inverted image is formed just below the object and is also of a focal length away from the lens. F1 and F2 are the focal points of the lens.

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Technique 2: Using the conjugate foci method

Instructions: View the 2nd segment of the video, “CSEC Physics Virtual Lab (YouTube Video),” in D2L. Use the pause button when necessary so that you can read measurements. Do not use the measurements given by the video, as they do not give the correct number of significant figures and do not include uncertainties.

Data:

Object position Xo (cm)

Screen position Xi (cm)

Lens position T1 (cm)

Lens position T2 (cm)

± ± ± ±

Data Analysis:

1) Calculate in the space below the distance between the object and screen, D (cm), and the distance between the lens positions, d (cm). Also, show calculations of the uncertainties, σD and σd. (Hint: See Lab1 Lecture Part I, slide #9, Propagation of error in calculations, case 1, sum and difference. For example, D = Xi – Xo. So, σD is calculated using the equation for the

case of sum and difference: 𝑅 = 𝑎𝑥 ± 𝑏𝑦, σ𝑅 = �𝑎2(σ𝑥)2 + 𝑏2�σ𝑦� 2 .)

2) Calculate in the space below the focal length f using the equation f = (D2 – d2)/(4D). Also, show calculation of the uncertainty, σf. (Hint: Since f is a function of D and d, use the method discussed in Lab1 Lecture Part I, slide #9, Propagation of error in calculations,

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case 3, general functions, 𝑅 = 𝑅(𝑥, 𝑦), σ𝑅 = �� ∂𝑅 ∂𝑥 � 2

(σ𝑥)2 + � ∂𝑅 ∂𝑦 � 2 �σ𝑦�

2 . You will need

to take partial derivatives.)

3) Derive equation, f = (D2 – d2)/(4D), from the thin-lens equation, 1/o + 1/i = 1/f, where o and i are the object and image distances, respectively. Use the figure below to help you. (Hint: As shown in the diagram, o + i = D, independent of which position you refer to. First, substitute o with o = D – i in the thin-lens equation. Second, rearrange terms to obtain a quadratic equation of i. Next, solve for i to get solutions, i1 and i2. Finally, set i1 – i2 = d, rearrange terms and you will be able to derive the equation required.) Show your derivation in the space below.

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Conclusion:

The focal length of the converging lens is found to be __________________________.

(Note: Make sure to include the correct number of significant digits in the reported value AND include the uncertainty in the stated result.)

Part B: Determine the focal length f of a diverging lens

Technique: Using a combination of converging and diverging lenses.

Instructions: Use the figure below to complete the data table.

Data:

Position of Diverging Lens XDL (cm)

Position of Image I1 XI1 (cm)

Position of Image I2 XI2 (cm)

± ± ±

0 45.00 cm 60.00 cm 80.02 cm 128.55 cm

Optical Bench Tape Measure (Smallest Division = 0.1 cm)

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Data Analysis:

1) Calculate in the space below the object distance o and image distance i of the diverging lens (DL). Also, show calculations of the uncertainties, σo and σi.

2) Calculate in the space below the focal length f of the diverging lens (DL) using the thin- lens equation, 1/o + 1/i = 1/f. Also, show calculations of the uncertainty, σf. (Hint: Study Example 2 in Lab1 Lecture Part I for help.)

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3) Draw a ray diagram for the lens combination below to show the final image formed.

Clearly show all the rays with arrows indicating direction. F1 and F1’ are the focal points of the converging lens (CL), and F2 and F2’ are the focal points of the diverging lens (DL).

Conclusion:

The focal length of the diverging lens is found to be __________________________. (Note: Make sure to include the correct number of significant digits in the reported value AND include the uncertainty in the stated result.)