PHYS2426 – Engineering Physics II

Image Formation with Thin Lenses

Leader: _________________________ Recorder: __________________________

Skeptic: _________________________ Encourager: ________________________

Materials

Optics Bench 100 mm lens

Light Source -150 mm lens

Screen Post-it note

White paper Ruler

Introduction

In this lab we examine several different examples of image formation as predicted by the thin lens formula, . (1) Our apparatus will consist of an optics bench, lenses in lens holders, a screen to project images, and a light source.

Part 1 – The Image of an Object at ∞

A distant object such as the sun, a distant building, or mountains off in the distance can be treated as though it is infinitely far away.

Q1. If an object is infinitely far away, explain why the rays coming from that object incident on a lens can be treated as parallel. (Drawing a picture may help.)

Q2. If the rays from a distant object incident on a converging lens are parallel, then where will the image be formed?

Q3. Draw a ray diagram showing the formation of the image.

With the lights in the room off, use the 100 mm converging lens to form the image of a distant object such as the window on a white piece of paper. Measure the distance from the lens to the image.

d_i = ___________

Q4. Use your image distance to estimate the focal length of the lens

f =

This is a common method for quickly determining the focal length of a lens, although it is not particularly accurate.

Q5. Find the % difference between the focal length of the lens that you estimated in Q4 and the value listed on the lens.

Q6. Comment on any reasonable sources of error that might occur in determining the focal length of the lens in this manner. Be specific and don’t use meaningless collectives.

Part 2 – The Image of an Object at the Focal Point

Place the light source at one end of the optical bench and the screen at the other end. Place the 100 mm focal length lens squarely in the optics bench a distance of 15 cm from the light source. Move the screen until you can find the image of the light source. The image should appear sharp.

Q7. Is the image real or virtual? Explain how you know.

Move the lens 1 cm closer to the light source and find the image again.

Q8. In what direction did you have to move the screen to find the image?

Move the lens 1 cm closer to the light source and find the image again.

Q9. In what direction did you have to move the screen to find the image?

Move the lens 1 cm closer to the light source and find the image again.

Q10. In what direction did you have to move the screen to find the image?

Move the lens 1 cm closer to the light source and find the image again.

Q11. In what direction did you have to move the screen to find the image?

Q12. As you move the object closer to the lens, how does the image location change?

Slowly slide the lens forward. Find the position of the object at which you just can no longer find the image. Note the image will move beyond the optics bench at some point.

Q13. Measure the distance from the light source to the lens.

d_o =

Q14. Where is the image located at this point?

Q15. How is the distance you measured related to the focal length? Explain.

Q16. Record your estimate for the focal length from this procedure.

f =

Q17. Draw a ray diagram for the formation of the image at this point.

Q18. Find the % difference between the focal length of the lens that you estimated in Q16 and the value listed on the lens.

Q19. Comment on any reasonable sources of error that might occur in determining the focal length of the lens in this manner.

Part 3 - Real Image Formation with a Converging Lens

Measure and record the height of the arrow on the light source

Q20. h_o = ______________________

Place the object 40 cm from the lens. Move the screen until you find the image.

Q21. Record the distance from the lens to the screen at which you found the image.

Q22. You may have noticed that there is a little uncertainty in locating the image. However, move the screen 5 cm away from where you found the image. Is the image still sharp at that point?

Q23. Does the image form anywhere you put the screen or only when the screen is placed at a certain location?

Q24. What is the focal length for this lens? Is the image formed at a distance equal to the focal length in this case?

Heasure and record the height of the image in this case

Q25. h_i = _________________

Q26. Use the measured heights to determine the magnification of the image. If the image is inverted be sure to make the magnification negative.

Q27. Now position the object at a distance of 20 cm from the lens. Move the screen to find the image and record the distance from the lens to the image.

Q28. Is the image located at the same distance from the lens as when the object was 40 cm from the lens?

Measure and record the height of the image in this case

Q29. h_i = _________________

Q30. Use the measured heights to determine the magnification of the image. If the image

Q31. Answer the following true or false. The image is always formed at the focal point of the lens. Explain.

Q32. In the space below use the thin lens equation and the magnification equation to calculate the location and the magnification of the image formed by the 100 mm focal length lens for each of the following object distances i) 40 cm, ii) 20 cm

Record your results

i) d_i = ii) d_i =

M = M =

Q33. Determine the % difference between the measured values and your calculated values

%difference d= %difference d=

%difference M= %difference M=

Q34. Draw a ray diagram showing the formation of the image for i) and ii). Explain why you only need to draw one ray diagram to qualitatively show the formation of the image for both i) and ii).

Part 4 – The Parallax Method

Place your head at the edge of the lab table facing towards the center of the table and close one eye. Have a person in your group drop a small scrap of paper about 1 cm in diameter onto the table several feet from you. Keeping your head in the same position and very still and keeping one eye closed, try and put your index finger on the scrap of paper. Repeat several times dropping the scrap of paper at different distances from you. Have each person in your group try.

Q35. Did you always place your finger on the scrap of paper or did you frequently miss?

Q36. When you missed, would you say that you missed in front/behind the paper or did you miss to the side?

Q38. If you missed to the front/back were you able to find the direct line of sight to the paper?

Q39. Can you locate an object with a single line of sight or do you need two lines of sight to it?

Q40. Draw a diagram showing a single ray from the object to your eye. Does the single ray by itself show the location of the image?

Try locating the piece of paper again, but this time have both eyes open with your head at table level.

Q41. Can you more successfully place your finger on the paper with two eyes?

Q42. Draw a ray diagram with a ray coming from the paper to each eye.

Q43. Does this ray diagram show the location of the object? Explain.

Hold a pencil or pen vertically in each hand with one directly above the other. Close one eye and shift your head horizontally back and forth.

Q44. Do the pencils appear to move relative to the table?

Q45. Do the pencils appear to move relative to each other?

Move the upper pencil several inches forward of the lower one.

Shift your head horizontally back and forth again.

Q46. Do the pencils appear to move relative to each other? In what way?

Move the pencils so that the lower one is several inches forward of the upper one.

Shift your head horizontally back and forth again.

Q47. Do the pencils appear to move relative to each other? In what way?

This idea can be used to locate one object relative to another.

Q48. When the objects are in a line when you shift your head what is their relative motion?

Q49. When one object is in front of a second, how does it appear to move with respect to the other when you shift your head?

Q50. Use these observations to devise a method for determining if two objects are at the same distance from an observer. We will refer to this method as the parallax method. Describe your method in the space below. Verify your method with your instructor since you will use it several times in the remainder of this lab activity.

Part 5 – Virtual Image Formation by a Converging Lens

Position the object so that it is 6 cm from the lens. Use the screen to examine the light coming from the lens.

Q51. Is the light diverging or converging?

Q52. If the light is diverging, where do you have to look to find the image?

Remove the screen to view the image. Look through the lens towards the light source.

Q53. Are you looking at the object or the image? Give observational evidence to support your answer.

Q54. Use the parallax method to locate the image. Hint: Make sure that the object you are holding above the image is above the lens, or else you will be looking at an image of that as well.

Q55. Record your result for the image distance d_i =

Q56. Use the thin lens equation to determine the location and magnification of the image for this case. Show your work in the space below.

d_i =

Q57. Determine the percent difference between the measured and calculated image distances.

% difference =

Q58. Qualitatively does the magnification of the image seem to agree you’re your calculation? Specifically is the orientation and relative size of the image compared to the object correct?

Q59. Comment on how accurate you think the parallax method is. Identify any likely sources of error. Be specific.

Q60. Draw a ray diagram showing the formation of the image for this case.

Part 6 - What Rays are Needed to Form the Image?

It was stated in class that the rays chosen when we draw a ray diagram are only chosen for the ease of drawing the diagram. The image is formed from any and all of the rays. We will explore that idea. Answer the following question first before attempting the experiment.

P61. If we place a Post-it-Note so that it covers half of the object, what will the image look like?

Place the 100 mm focal length lens in the holder at a distance of 20 cm from the object. Find the image on the screen. Place a Post-it Note so that it covers half of the object.

Q62. Describe the appearance of the image after the Post-it-Note was placed over half of the object.

Q63. Does the full image form or only part of it?

Make the following prediction before making the observation.

P64. If we place a Post-it-Note so that it covers half of the lens, what will the image look like?

Place the 100 mm focal length lens in the holder at a distance of 20 cm from the object. Find the image on the screen. Place a Post-it Note so that it covers half of the lens.

Q65. Describe the appearance of the image after the Post-it-Note was placed on the lens.

Q66. Does the full image form or only part of it?

Q67. If the full image formed how is it different? Try moving the Post-it-Note on and off to compare.

Q68. Summarize your observations by completing the following. When the lens was half covered, __________ of the image was formed, but its ___________ was decreased.

Q69. Draw a ray diagram showing for the case when half the object was covered why the image that was formed appeared the way it did.

Q70. Draw a ray diagram showing for the case when half the lens was half covered why the image that was formed appeared the way it did.

Part 7 - Image formation by a concave lens

Place a -15 cm focal length lens in the holder 30 cm in front of the object. Use the screen to examine the light passing through the lens.

Q71. Is the light converging or diverging?

Q72. Where do you have to look to see the image?

Q73. Use the parallax method to find the location of the image.

d_i =

Q74. Use the thin lens equation to predict the image location and magnification.

Q75. Qualitatively does the magnification of the image seem to agree with your calculation? Specifically is the orientation and relative size of the image compared to the object correct?

Q76. Compute the percent difference between the measured and calculated image locations.

%difference =

Q77. Draw a ray diagram showing the image formation.