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Experiment 11: Thin Lenses The goal of this lab is to explore formation of images by thin lenses

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Experiment 11: Thin Lenses

The goal of this lab is to explore formation of images by thin lenses.

Theory

For a thin lens with focal length f

 , it can be shown that

 

1f= 1do+idi

(1)

 

where do

 and di

 are the object and image distances respectively. This is called the thin-lens equation. The object distance is measured from the object to the lens, and the image distance is measured from the image to the lens.

 

In this equation, the focal length f

 should be taken with sign “plus” in the case of converging lens and with the sign “minus” in the case of diverging lens. The object distance do

 is positive number corresponding to the object position to the left of the lens. The image distance di

 found from the lens equation could be either positive or negative number. Distance di>0

 corresponds to the image positioned to the right of the lens (real image), whereas di<0

 corresponds to the image positioned to the left of the lens (virtual image).

 

Lateral magnification, M

, is defined as the ratio of the image height, hi

, to object height, ho

:

 

M=hiho

(2)

 

The value of M

 can be found as

 

                                                                                     M=-dido

                                                                            (3)

 

In Eq. (3), M

 can be either positive or negative number Positive values of M

 correspond to the upright image having the same orientation as an object, whereas negative values of M

 correspond to the inverted image having orientation opposite to that of the object.

 

 

In this lab, we’ll explore how thin converging and diverging lenses form the images at different positions of an object relative to the lens

 

 

Procedure

Physics Simulations: Concave and Convex Lenses

https://ophysics.com/l12.html

 

Object height and position. Click and hold (purple circle). left or right: change object position. up or down: object height.

How to use the Simulation

1. Change object height, position and focal point

 

Change focal point. Click and hold (purple circle). left or right: change focal position.

 

Experiment

Part A. Converging lens (f>0

)

 

1. Set do=12

   

    units ho=1

   

    unit, and f=5

   

    units. Find the image distance di

   

   and the image size hi

   

      Record the value of di

   

    and the lateral magnification M=hiho

   

    in the data table.
2. Repeat step 1 as you decrease the object distance to 11, 9, 3, 2, and 1 unit. Record your results in the data table.
3. Calculate di

   

    and M

   

    using Eqs. (1)-(3) and record your results in the table.

 

do	12	11	9	3	2	1
di , exp.
M , exp.
di , calc.
M , calc.

 

Analysis:

1. At what values of do

   

    the image is real? At what values of do

   

    the image is virtual? How do you know? Explain your answer.

 

 

2. At what values of do

   

    the image is upright? At what values of do

   

    the image is inverted? How do you know? Explain your answer.

 

 

 

 

 

Part A. Diverging lens (f<0

)

 

4. Set do=12

   

    units ho=2

   

    units, and f=-6

   

    units. Find the image distance di

   

   and the image size hi

   

      Record the value of di

   

    and the lateral magnification M=hiho

   

    in the data table.
5. Repeat step 1 as you decrease the object distance to 10, 8, 6, 4, and 2 units. Record your results in the data table.
6. Calculate di

   

    and M

   

    using Eqs. (1)-(3) and record your results in the table.

 

do	12	10	8	6	4	2
di , exp.
M , exp.
di , calc.
M , calc.

 

Analysis:

1. At what values of do

   

    the image is real? At what values of do

   

    the image is virtual? How do you know? Explain your answer.

 

 

2. At what values of do

   

    the image is upright? At what values of do

   

    the image is inverted? How do you know? Explain your answer.