Purpose  To analyze, through theoretical and experimental methods, the relative luminescence of a series of images produced by multiple reflections in a decorative glass lamp The number of visible images can be used to measure the sensitivity range of the eye

Background  Glass oil lamp from Curry Club Restaurant, East Setauket  Inner walls of the glass have a partially reflective coating  Dimensions: 6.5in x 3in x 3in  Glass walls are 0.25in thick and have a brown tint 6.5 in 3 in 0.25 in 11 images

Background (cont.) 2nd image 3rd image 4th image  When the flame is viewed at eye level, a series of flame images can be seen  Each consecutive image is dimmer than the last and images can be seen in a dark room  The nth image is produced by n-1 reflections  The reflectance of the inner wall determines the relative brightness of the image 1st image Top View

Procedure - Part 1 Outer Surface Inner Surface  An He-Ne laser and a photo detector were used to measure I 1, I 2, I 3, and I 4 to calculate the reflectance of the inner and outer surface and the absorption (t)  Incoming light split between absorption, reflection, and transmission I1I1 I4I4 I2I2 I3I3 I5I5 I6I6 I7I7 I8I8 R o = I 2 / I 1 R i = I 7 / I 6 t = I 6 / I 5

Measured Intensity Values First Run Second Run Ratio*Average I1I1 245 mA mA I2I2 7.9 mA mA I3I μA μA I4I μA μA * Ratio of second run to first run. The second run values are lower because the laser power decreased after warm-up but are consistent with the first run.

 The values of R i, R o, and t were derived from a set of equations that contained the measured values of I 1, I 2, I 3, and I 4.  t = 1-a and a = absorption ratio  I 5 = I 1 - I 2  I 6 = t*I 5 = t*(I 1 - I 2 )  I 7 = I 6 - I 3 = t*(I 1 - I 2 )-I 3  I 8 = t*I 7 = I 4 + I 8 *(I 2 /I 1 )  t 2 *(I 1 - I 2 )-t*I 3 - I 4 /(1 - (I 2 /I 1 )) = 0  R o = I 2 /I 1  R i = I 7 /I 6 = 1 - I 3 /(t*(I 1 - I 2 )) Analysis and Results Results: R o = 3.2% t = 40.8% R i = 42.5%

Procedure - Part 2  Laser beam allowed to travel through the lamp  5 visible spots  Photo detector used to measure their intensities in Volts using a 100 kΩ resistor & iris used to isolate the images  The ratio of the spot intensities is R i 2  R i 2 = % Laser Lamp 5 spots of decreasing intensity IrisPhoto Detector

Discussion / Conclusion  The reflectance of the inner surface of the glass lamp (R i ) equals the relative luminescence between the flame images  R i was measured using two independent methods and the 2 values are in very good agreement  R i = 43.0 ± 0.5%  This value predicts the relative luminescence of the candle flame as shown in the graph below  The nth image is approximately (0.43) n times as bright as the first image  The 11 th image is 10, 760 times brighter than the first  Therefore, the human eye can perceive a range of about 10,000 in intensity at a single instant

Future Study  Testing human visual sensitivity  Determining an optimum reflection-transmittance ratio (applications for sunglasses, tinted glass, etc.)  Analyzing or designing “one-way” mirrors  Analyzing laser cavities