Optics: Converging Lenses Experiment

J Heezy

Image Distance vs. Object Distance

• Purpose: find relationship between image distance and object distance (Di vs. Do)

• Procedure: Started light source (object) 15 focal lengths away from lens and found focused image with screen, moved object closer to lens (decreased Do) and found corresponding Di that presented a focused image on the screen

Materials

• Track• Light Source• Meterstick• Converging Lens• Screen/Location for Image Formation• Distant powerline

Data

Type 1 analysis

Type 1 analysis

linearizedType 1 analysis

Mathematical analysisdo = object distance, di = image distance, xo = adjusted object

distance, xi = adj image distancey 1/x∝xi = k/xok = 0.03574m^2 (per LoggerPro)k = f2 (0.202m)2 = 0.0408Model: xi = f2/xoAnd to make the model more useful:di-f = f2/(do-f)dido - dif - dof - f2 = f2

dido = dif + dof1 = f/do + f/diModel = 1/f = 1/do + 1/di

Type 2 analysis

Type 2 analysis

Type 2 analysis

Mathematical analysis

do = object distance, di = image distance

y=mx +b1/di=k*(1/do)+bk = -1.001 (per LoggerPro)b = 5.054 1/m (per LoggerPro)b=1/f (f=0.202 m)Model: 1/f = 1/di + 1/do

Image Height vs. Object Distance

• Purpose: Find a relationship between image height and object distance (Hi vs. Do)

• Procedure: Started light source (object) 15 focal lengths away from lens and found focused image with screen, moved object closer to lens (decreased Do) and found corresponding Hi that presented a focused image on the screen

Materials

• Track• Light Source• Meterstick• Converging Lens• Screen/Location for Image Formation• Distant powerline

Data

Type 1 analysis

Type 1 analysis

Type 1 analysis

Mathematical Analysis

do = object distance, hi = image height, xo = adjusted object distance

y 1/x∝hi = k/xok = 0.03574 (per LoggerPro)k = f2 (0.202m)2 = 0.0408Model: hi = f2/xoAnd to make the model more useful:hi = f2/(do-f)