(JL)^2 [aka Jackie and Jocelyn]

 Determine the relationship between object distance and image distance for real images in a concave spherical mirror  Determine the relationship between object height and image height for a set object distance

 The inverse of image distance will be linearly related to the inverse of object distance  The object height will be directly proportional to image height

 Focal point – where rays parallel to the principal axis come to a focus  Focal length – distance between focal point and center of the mirror

 Set curved mirror on track facing an open window.  Set screen on track between window and mirror.  Adjust distance between screen and mirror until focused image (far away object through window, like a power pole) appears on the screen. Measure this distance with meter stick.

 Place object 15 focal lengths from mirror using cart tracks.  Place the screen between mirror and object/light source (see diagram).  Move the screen until a focused image of the object appears on the screen.  Measure and record the image height that appears on the screen and the distance between the screen and the mirror (image distance).  Decrease object distance by 1 focal length and repeat process until 3 focal lengths away from mirror.  Change distance increments to 5 cm. Continue process until 2 focal lengths away.  Reduce distance increments to 1 cm. Continue process until 1 cm less than 1 focal length away.

1/object distance = (1/d o ) Example: 1/d o = 1/390 cm 1/d o = /cm 1/image distance = (1/d i ) Example: 1/d i = 25 cm 1/d i = /cm

1/d i  1/Image distance 1/d o  1/object distance y = mx + b 1/d i = k (1/d o ) + b k = Δ(1/d i )/Δ(1/d o ) k = /cm / 1/cm k = b = /cm 1/d i = (1/d o ) /cm All slopes and values by LoggerPro

Accepted Value: 1 Experimental Value (Source: magnitude of 1/d i vs. 1/d o graph slope): 1.05 ABS error: ǀ Accepted value-Experimental value ǀ ǀ 1 – 1.05 ǀ 0.05 Relative error: ABS/accepted value (0.05)/ (1) 0.05  5% error

Accepted Value: 1/focal length = 1/26 cm = /cm Experimental Value (Source: y-intercept of 1/d i vs. 1/d o graph): /cm ABS error: ǀ Accepted value-Experimental value ǀ ǀ /cm – /cm ǀ /cm Relative error: ABS/accepted value ( /cm)/ ( /cm)  8.8% error

 The method for taking data for this part largely relied on eyeballing distances and heights, so that was probably the largest source of error.  Also, for distance, we used a ruler to measure distances, which we had to constantly reset— so distances may not have been consistent, esp. with room darkness.

1/d i = b - k(1/d o ) k = 1 b = 1/f 1/d i = 1/f - (1/d o ) 1/d i + 1/d o = 1/f

 Place mirror on stand, at head of track.  Use large lamp as light source. Place smallest arrow card in front holder. Move light source 1.5 focal lengths from mirror.  Place screen between light source and mirror. Do not block light source. Adjust mirror so that image appears on screen.  Move screen until image focuses.  Measure image height and object height with ruler.  Repeat process for all arrow cards, recording the height of actual arrow as well.  Move light source until it is 2.5 focal lengths from the mirror and repeat entire process.

h i  Image height h o  Object height h i ∝ h o y = mx h i = k (h o ) k = Δh i / Δh o k = 1.89 cm/cm k = 1.89 h i = 1.89 h o All slopes and values by LoggerPro

Accepted Value: f/(d o – f) = 26 cm / [1.5 (26cm) – 26 cm] = 2 Experimental Value (Source: magnitude of h i vs. h o graph slope): 1.89 ABS error: ǀ Accepted value-Experimental value ǀ ǀ 2 – 1.89 ǀ 0.11 Relative error: ABS/accepted value 0.11/  5.5% error

 Same as in part 1: eyeballing distances was the largest source of error, as well as estimating where the image focused exactly.

h i = k(h o ) k = f/(d o – f) h i = [f/(d o – f)](h o )

h i  Image height h o  Object height h i ∝ h o y = mx h i = k (h o ) k = Δh i / Δh o k = cm/cm k = h i = h o All slopes and values by LoggerPro

Accepted Value: f/(d o – f) = 26 cm / [2.5 (26cm) – 26 cm] = Experimental Value (Source: magnitude of h i vs. h o graph slope): ABS error: ǀ Accepted value-Experimental value ǀ ǀ – ǀ Relative error: ABS/accepted value 0.074/  11% error

 Same as in parts 1 and 2: eyeballing distances was the largest source of error, as well as estimating where the image focused exactly.

[This might possibly look familiar.] h i = k(h o ) k = f/(d o – f) h i = [f/(d o – f)](h o )

From experiments 2 and 3: h i = [f/(d o – f)](h o ) h i / h o = f/(d o – f) From experiment 1: 1/d i + 1/d o = 1/f So: 1/d i = 1/f- 1/d o 1/d i = d o /fd o - f/fd o 1/d i = (d o - f)/fd o d o /d i = (d o - f)/f d i /d o = f/(d o - f) h i / h o = d i /d o