Pinhole Experiments

Scott + Harrison

Purpose- To investigate the relationship between object distance

and image height while image distance and object height are constant.

- To investigate the relationship between object height and image height while object distance and image distance are constant

- To investigate the relationship between image distance and and image height while maintaining a constant object height and object distance

- To investigate the effects on the image by increasing the diameter of the pinhole and creating more than one pinholes

Hypothesis- If we decrease the object distance, then the image height

will increase.- If we increase the object height, the image height will

increase- If we increase the image distance, then the object

distance will increase- If we increase the number of pinholes, multiple images will

form- If we increase the diameter of the hole, the image will be

less focused

Equipment/DiagramLight source for holding cards, pinhole camera (a box with

one end open and the other with a translucent screen inside a larger box with one end open and a square hole in the other), arrow cards, meter stick, aluminum foil

Procedure

1. Cover a hole with aluminum foil and poke a hole with a pin in it.2. Face the pinhole at a bright object (not necessarily a lightbulb).3. Set a screen behind the pinhole for the image to be projected on.4. Vary the distance of the object from the pinhole, while keeping the image

distance from the pinhole and object height constant.5. Vary the distance of the screen (thus the image) from the pinhole, while

keeping the object distance and object height constant.6. Vary the height of the object (arrow), while keeping the image distance and

object distance constant.7. Poke some more pinholes and observe the effect.8. Increase the size of a pinhole and observe the effect.

Hi vs Do Hi is proportional to 1/Do

Exp 1 Mathematical Analysis + ErrorExp 1:Image Height-->Hi, Object Distance-->Do, (Di and Ho are held constant)

Hi α 1/DoHi = k*1/Dok = 0.01455m^2 (calc by Logger Pro)

Hi = 0.01455m^2 * 1/Do

hi = h0*di * (1/d0), slope = h0*di = .085 m*.165 m = .01403 m2

Accepted Value= .01403 m2

Experimental Value= .01455 m2

Absolute Error = | Acc-Exp |Absolute Error=| .01403 m2- .01455 m2|Absolute Error= .00052 m2

Relative Error= Abs /AccRelative Error= .00052 m2 / .01403 m2

Relative Error= 3.71%

Hi vs Di

Hi is proportional to Di

Exp 2 Mathematical Analysis + Error

Exp 2:Image Height-->Hi, Image Distance--> Di, (Do and Ho are held constant)

Hi α DiHi = k* Dik = 0.1543m/m (calc by Logger Pro)

Hi = 0.1543m/m * Ho

h0 = .085 m, h0 = .56 mhi = h0/d0* di, slope = h0/d0 = .085 m/.56 m = .1518Accepted Value= .1518Experimental Value= .1543

Absolute Error = | Acc-Exp |Absolute Error=| .1518- .1543|Absolute Error= .0025

Relative Error= Abs /AccRelative Error= .0025 / .1518Relative Error= 1.65%

Hi vs Ho

Hi is proportional to Ho

Exp 3 Mathematical Analysis + ErrorExp 3:Image Height-->Hi, Object Height-->Ho

Hi α HoHi = k* Hok = 0.8527m/m (calc by Logger Pro)

Hi = 0.8527m/m * HoExp 3 Image Height vs Object Heightdi = .165 m, di = .20 m, d0 = .56 m

hi = di/d0 * h0, slope = di/d0 = .165 m/.20 m = .8250

Accepted Value= .8527Experimental Value= .8250

Absolute Error = | Acc-Exp |Absolute Error=| .8250- .8527|Absolute Error= .0277

Relative Error= Abs /AccRelative Error= .0277 / .8250

Relative Error= 3.36%

Similar Triangle Proof

Ray Diagrams

Original

Increasing Object Distance, Decrease Image Height

If we increase the object height, we increase the image height.

All ray diagrams are based on idea that light travels as a straight line.

If we increase the image height, we increase the image distance

Ray DiagramsMultiple Pinholes

Bigger PinholeMultiple Images

Blurred

Animation

http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=38.0