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Pinhole Camera Investigation By Oscar G.M and David Mayer 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. 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. Equipment Setup Part 1: Image Height vs. Object Distance Image Distance: 0.16 m Object Height: 0.023m Mathematical Analysis 1. Image Height vs. Object Distance Image Height Hi Object Distance do 2. Hi α 1/ do 3. Hi = k* 1/ do 4. k = ∆ Hi / ∆ 1/ do 5. k = 0.00399 m/1/m 6. 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 . Meaning? 0.023m * 0.16 m = image distance * object height Image distance = di And Object height = Ho So Slope= Ho* di Error Calculations Accepted Value=0.16m*0.023m=0.00368m2 Experimental Value=0.00400m2 Part 2: Image Height vs. Object Height Object Distance: 0.20 m Image Distance: 0.16 m Mathematical Analysis 1. Image Height vs. Object Height Image Height Hi Object Height Ho 2. Hi α Ho 3. Hi = k* Ho 4. k = ∆ Hi / ∆ Ho 5. k = 0.812 mm/mm 6. 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 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 Error Calculations Accepted Value=0.16m/0.2m=0.800 Experimental Value=0.812 Part 3: Image Height vs. Image Distance Object Height: 0.023 m Object Distance: 0.200 m Mathematical Analysis 1. Image Height vs. Image Distance Image Height Hi Image Distance di 2. Hi = α di 3. Hi = k*di 4. k = ∆ Hi / ∆ di 5. k = 0.100 m/m 6. 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 Meaning (last cheesy time)? 0.023m / 0.200 m = object height / object distance So Slope= Ho/ do Error Calculations Accepted Value=0.0230m/0.200m=0.115 Experimental Value=0.100 The Basic Principle Pinhole Ho Object Hi do Light Source with rays di Part 1: Changing Object Distance Original Ho Hi do di Part 2: Changing Object Height Original Ho Hi do di Part 3: Changing Image Distance Original Ho do di Hi 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 Geometry Ho θ θ Hi do di More Pinholes Bigger Diameter Pinhole Bigger Hole = Brighter, Blurrier Image