Pinhole Camera Investigation

1. Pinhole Camera Investigation By Oscar G.M and David Mayer

2. Introduction Purposes: • To investigate the relationship between object distance and image height while maintaining a constant image distance, and a constant object height. • To investigate the relationship between object height and image height while maintaining a a constant object distance, and a constant image distance. • To investigate the relationship between image distance and image height while maintaining a constant object height, and a constant object distance. • To observe the effects of increasing the diameter of the pinhole, and creating more than one pinhole.

3. Hypotheses • If we decrease the object distance, then the image height will increase. • If we increase the object height, then the image height will increase as well. • If we increase the image distance then the object distance will increase as well.

4. Equipment

6. Setup

9. Part 1: Image Height vs. Object Distance Image Distance: 0.16 m Object Height: 0.023m

12. Mathematical Analysis Image Height vs. Object Distance • Image Height  Hi Object Distance  do • Hi α 1/ do • Hi = k* 1/ do • k = ∆ Hi / ∆ 1/ do • k = 0.00399 m/1/m • Hi = 0.00399 m/1/m * 1/ do Let’s look at those units… m/(1/m)  m*(m/1)  m2 Hmm, m2 … what were our constants again? Image distance: 0.16 m, object Height: 0.023m. m*m  m2 . 0.023m * 0.16 m = 0.00368 m2 .

13. Meaning? 0.023m * 0.16 m = image distance * object height Image distance = di And Object height = Ho So Slope= Ho* di

14. Error Calculations Accepted Value=0.16m*0.023m=0.00368m2 Experimental Value=0.00400m2

15. Part 2: Image Height vs. Object Height Object Distance: 0.20 m Image Distance: 0.16 m

17. Mathematical Analysis Image Height vs. Object Height • Image Height  Hi Object Height  Ho • Hi α Ho • Hi = k* Ho • k = ∆ Hi / ∆ Ho • k = 0.812 mm/mm • Hi = 0.812 mm/mm * Ho Let’s look at those units once more… mm/mm  1 This looks like a ratio…our constants were object distance: 0.20 m, image distance: 0.16 m Constant / Constant = 0.812

18. Meaning? The only way for this to occur is if we divide the smaller number by the larger number to give us something less than 1. 0.16 m / 0.200 m = 0.800 Slope= di/do

19. Error Calculations Accepted Value=0.16m/0.2m=0.800 Experimental Value=0.812

20. Part 3: Image Height vs. Image Distance Object Height: 0.023 m Object Distance: 0.200 m

22. Mathematical Analysis Image Height vs. Image Distance • Image Height  Hi Image Distance  di • Hi = α di • Hi = k*di • k = ∆ Hi / ∆ di • k = 0.100 m/m • Hi = 0.100 m/m *di Looks like a ratio once more…our constants were object height: 0.023 m, object distance: 0.200 m Constant / Constant = 0.100

23. Meaning (last cheesy time)? 0.023m / 0.200 m = object height / object distance So Slope= Ho/ do

24. Error Calculations Accepted Value=0.0230m/0.200m=0.115 Experimental Value=0.100

25. The Basic Principle Pinhole Ho Object Hi do di Light Source with rays

26. Part 1: Changing Object Distance Original Ho Hi di do

27. Part 2: Changing Object Height Original Ho Hi do di

28. Part 3: Changing Image Distance Original Ho Hi do di

29. 2 More Ways to See This Relationship Joint Variation: Hi α 1/ do Hi α Ho Hi α di Hi α Ho * di /do Hi = Ho * di /do There was no constant of proportionality

30. Geometry Ho θ θ Hi do di

31. More Pinholes

33. Bigger Diameter Pinhole Bigger Hole = Brighter, Blurrier Image

35. The End