Measuring Planck's Constant Sitting at Your Desk (25 pts)

In this problem, you will use the ``night-time speckle effect'' and then use that effect to make an arm-chair estimate of the value of Planck's constant h.

When we observe objects at low illuminations we see ``static'' similar to what one might see on a television set. In this question we investigate the issue of whether this might be due to the randomness in the arrival of photons, so called ``photon shot noise.''

We will use the following rough observations about the human eye, which you could make yourself.

1. The ``response/sampling'' time for the human eye is somewhere between the imperceptible cycle time of fluorescent lighting and the noticeable flicker of old-time movies at 15 frames per second,
2. The resolution of the human eye is (the angle of a single pixel on a CRT at a viewing distance about 30 cm). This corresponds to a solid viewing angle of each receptor of about st. rad.
3. The radius of the pupil (the aperture through which light enters the eye) is 0.4 cm making the total area over which it gathers light
4. The human eye can perceive fluctuations in brightness on the order of about f=3% of the power received. (8 bits is more than enough to digitally encode black and white pictures.)

• Photons released by the bulb
• Photons received by each receptor
• Fluctuations in each receptor
• Perception of the fluctuations
• Derivation of Planck's constant