PurposeTo analyze, through theoretical

and experimental methods, the relative luminescence of a series of images produced by multiple reflections in a decorative glass lampThe 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 in11 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 11-12 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 I1, I2, I3, and I4 to calculate the reflectance of the inner and outer surface and the absorption (t)

Incoming light split between absorption, reflection, and transmission

I1I4I2

I3

I5

I6I7

I8 Ro = I2 / I1

Ri = I7 / I6

t = I6 / I5

Measured Intensity Values

First RunSecond

RunRatio* Average

I1 245 mA 233.8 0.95 239.4 mA

I2 7.9 mA 7.5 0.95 7.7 mA

I3 55.2 μA 53.5 0.97 54.4 μA

I4 16.3 μA 15.5 0.95 15.9 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 Ri, Ro, and t were derived from a set of equations that contained the measured values of I1, I2, I3, and I4.

t = 1-a and a = absorption ratio I5 = I1 - I2 I6 = t*I5 = t*(I1 - I2) I7 = I6 - I3 = t*(I1- I2)-I3 I8 = t*I7 = I4 + I8*(I2/I1) t2*(I1 - I2)-t*I3 - I4/(1 - (I2/I1)) = 0 Ro = I2/I1 Ri = I7/I6 = 1 - I3/(t*(I1 - I2))

Analysis and Results

Results:

Ro = 3.2%

t = 40.8%

Ri = 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 Ri

2

Ri2 = 19.099%

Laser

Lamp5 spots of decreasing intensity

Iris Photo Detector

Discussion / Conclusion The reflectance of the inner surface of the glass lamp

(Ri) equals the relative luminescence between the flame images

Ri was measured using two independent methods and the 2 values are in very good agreement

Ri = 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 11th 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