BE 518 F2017 Homework 1 SOLNS.pdf

# BE 518 F2017 Homework 1 SOLNS.pdf - 1(a What is the...

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(a) What is the wavelength of a 90.9 MHz radio wave? (b) What is the frequency in Hz of light with 550 nm wavelength (green)? (c) What is the speed of red light (l=650 nm) in water? SOLUTION (a) λ = c / ν = (3 * 10 8 m/s) / ( 90.9 * 10 6 s -1 ) = 3.3 m (b) ν = c/ λ = (3 * 10 8 m/s )/ (550 * 10 -9 m) = 5.45 * 10 14 Hz (c) Refractive index of water at 650 nm (from table): n = 1.331 c/n = 3 * 10 8 / 1.331 m/s = 2.25 * 10 8 m/s 1

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(a) How accurate, in percent, is the approximation sin q = q, for q = 0.1, 0.25, and .5? (b) Same question for tan q = q. theta sin(theta) error tan(theta) error 0.1 0.099833416 65 0.17% 0.100334672 1 -0.33% 0.25 0.247403959 3 1.05% 0.255341921 2 -2.09% 0.5 0.479425538 6 4.29% 0.546302489 8 -8.48% SOLUTION 2
Fermat’s principle or the principle of least time states that a

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• Fall '17
• refractive index, focal length

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