A student is given data captured from a digital camera; the scene viewed by the camera is a…

A student is given data captured from a digital camera; the scene viewed by the camera is a spherical frosted incandescent lamp that emits 1.2 W of power in the visible range. The lamp has a radius of 0.0175 m. The camera shutter speed has been adjusted so that the sensor is neither saturated nor starved; indeed, the values in the image are near the center of the camera’s pixel-value range, and can be assumed to be proportional to radiance. The value observed for pixels that lie in the lamp is 4000 (on a scale from 0 to 8191). The student wants to know the constant of proportionality between the radiance of arriving light and the sensor value. The student says, “The lamp is supposed to emit uniformly because of its frosting, so except for really tangential angles, we can figure that the radiance of all outgoing rays is constant. The area of the lamp is 4πr2 ≈ 0.000 962 m2; the hemisphere over which the light is radiated has solid angle measure approximately 6.28 sr, so the radiance, by division, is the power divided by the angle and the area, giving L ≈ 1.2 W/(0.000 962 m2 ∗ 6.28 sr) ≈ 0.006 W/m2sr. So to get the radiance L from the sensor value, we multiply by 0.006 4000 = 1. 5×10−6.” Critique the student’s approach, and give the correct answer.

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