EE372_Solutions1

# EE372_Solutions1 - EE372 Assignment 1 Solutions 1 Photons a...

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EE372 Assignment 1 Solutions 1. Photons a) A 50 kW FM radio station transmits annoying pop music at 95.1 MHz. What is the energy of each photon at this frequency in eV? Calculate the number of photons emitted from the antenna per second. b) A 1 kW CO 2 laser produces a beam with a wavelength of 10.6 μ m and is used to cut metal. What is the energy of each photon in eV? Calculate the number of photons emitted from the laser per second. c) A green LED produces 2 mW of light output at a wavelength of 530 nm. What is the energy of each photon in eV? Calculate the number of photons emitted from the LED per second. d) A synchrotron beam-line produces 5 × 10 11 photons / s with a photon energy of 9 keV. What is the wavelength of light produced and the total power of the beamline? Answer : a) E ph = = (6 . 63 × 10 - 34 J s)(95 . 1 × 10 6 Hz) = 6 . 31 × 10 - 26 J = 3 . 94 × 10 - 7 eV Φ = P/E ph = (50 × 10 3 W) / (6 . 31 × 10 - 26 J) = 7 . 92 × 10 29 photons / s b) E ph = hc/λ = (6 . 63 × 10 - 34 J s)(3 . 00 × 10 8 m / s) / (10 . 6 × 10 - 6 m) = 1 . 88 × 10 - 20 J = 0 . 117 eV Φ = P/E ph = (1 × 10 3 W) / (1 . 88 × 10 - 20 J) = 5 . 32 × 10 22 photons / s c) E ph = hc/λ = (6 . 63 × 10 - 34 J s)(3 . 00 × 10 8 m / s) / (530 × 10 - 9 m) = 3 . 75 × 10 - 19 J = 2 . 33 eV Φ = P/E ph = (2 × 10 - 3 W) / (3 . 75 × 10 - 19 J) = 5 . 33 × 10 15 photons / s d) E ph = 9 keV = 1 . 45 × 10 - 15 J λ = hc/E ph = (6 . 63 × 10 - 34 J s)(3 . 00 × 10 8 m / s) / (1 . 45 × 10 - 15 J) = 0 . 137 nm P = Φ E ph = (5 × 10 11 photons / s)(1 . 45 × 10 - 15 J) = 0 . 73 mW 2. Brightness The brightness of a light source depends not only on the optical power emitted but also on the ability of the human eye to perceive the light. The apparent brightness of a monochromatic source is proportional to the radiated power φ e times the eﬃciency of the eye to detect the wavelength η ( λ ). η is maximal and equal to one at 555 nm (green) and goes to 0 at the onset of the infrared and ultraviolet bands producing roughly a Gaussian shape (see Figure 3.46

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in the textbook). Brightness or luminous ﬂux φ u is measured in lumens (lm), and is deﬁned by φ u = 633(lm / W) * φ e * η One lumen of luminous ﬂux is obtained from a 1.58 mW light source emitting at 555 nm. A typical 60 W incandescent lamp provides roughly 900 lm. a) How much optical power must be produced by a red laser pointer (660 nm) to equal the same brightness as a 1 mW green laser pointer (530 nm)? Estimate η from the photopic curve of Figure 3.46. Calculate the number of photons emitted per second by each laser. b) If red light (660 nm) and green light (563 nm) of equal brightness are mixed the result is perceived as yellow. Calculate the ratio of red to green photons in the yellow light. Answer
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EE372_Solutions1 - EE372 Assignment 1 Solutions 1 Photons a...

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