This book is the solution manual to the textbook "A Modern Course in University Physics". It contains solutions to all the problems in the aforementioned textbook. This solution manual is a good companion to the textbook. In this solution manual, we work out every problem carefully and in detail. With this solution manual used in conjunction with the textbook, the reader can understand and grasp the physics ideas more quickly and deeply. Some of the problems are not purely exercises; they contain extension of the materials covered in the textbook. Some of the problems contain problem-solving techniques that are not covered in the textbook.
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1.1 Number of wavelengths between two points. A light wave of vacuum wavelength 500 nm travels from point A to point B that is a distance of 0.01 m away.
(1) If the space containing points A and B is vacuum, how many wavelengths span the space from A to B?
(2) If the region between points A and B is completely filled with glass of refractive index n = 1.5, how many wavelengths span the space from A to B?
Let DAB be the distance between points A and B, λ the vacuum wavelength, and λ′ the wavelength in glass.
(1) In vacuum, the number of wavelengths that span the space from A to B is
(2) Note that the frequency of a light beam remains unchanged no matter in which medium it travels. The wavelength of light in glass is given by
where v is the speed of light in glass and f and f′ are respectively the frequencies of light in vacuum and in glass with f′ = f. If the region between points A and B is completely filled with glass, the number of wavelengths that span the space from A to B is given by
1.2 Dispersion of fused silica. The wavelength-dependence of the refractive index of fused silica is given by
(1) At what wavelengths, does n diverge? If n is infinite for light of a particular wavelength, can the light of this wavelength propagate in fused silica?
(2) At what wavelengths, is n equal to unity?
(3) What is the value of n as λ → ∞?
(4) Plot n as a function of λ in the visible region for λ from 400 nm to 700 nm.
(1) From the given expression of n in terms of λ, we see that n diverges at λ ≈ 6.840 × 101, 1.162 × 102, and 9.896 × 103 nm. If n = ∞ for light of a particular wavelength, then v = c/n = 0, which implies that the light of this wavelength can not propagate in fused silica and will be absorbed.
(2) To find the wavelengths at which n = 1, we set the given expression for n2 to unity and obtain
From the above equation, we see that n = 1 at λ1 = 0. The other wavelengths at which n = 1 are to be solved from
The above equation is actually a quadratic algebraic equation in λ2. Simplifying the above equation, we have
where
α = B1 + B2 + B3,
β = − [B1(C2 +C3)+B2(C3+C1)+B3(C1+C2)],
γ = B1C2C3 + B2C3C1 + B3C1C2.
Solving for λ2 from Eq. (1.1), we obtain
Evaluating the above expression using the given values of constants, we obtain the following two positive solutions for λ
