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Question

A sensor is exposed for time t to a lamp of power P at distance l. The sensor has an opening that is 4d in diameter. Assuming all of the energy is given off as light, the number of photons entering the sensor if the wavelength of the light is λ is

A
N = Pλd2thcl2
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B
N = 4Pλd2thcl2
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C
N = Pλd2t4hcl2
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D
N = Pλd2t16hcl2
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Solution

The correct option is A N = Pλd2thcl2
E =hcλ
Number of photons emitted is Pthcλ = n0
n0= Pλthc
Since the radiation is spherically symmetric, so the number of photons entering the sensor is n0 times the ratio of aperture area to the area of sphere of radius l
N = n0π(2d2)4πl2 = Pλtd2hcl2

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