6 worked answers · short steps first, explanations when you need them
Chapter 10 Exercises
Textbook pages 273
Question 1
Monochromatic light of wavelength 589 nm is incident from air on a water surface. What are the wavelength, frequency, and speed of (a) reflected light and (b) refracted light? Take the refractive index of water as 1.33.
Steps only
f=c/λ=5.09×10¹⁴ Hz. In water v=c/1.33=2.26×10⁸ m/s and λ=589/1.33≈443 nm; f does not change.
State the shape of the wavefront in each case: (a) light diverging from a point source, (b) light emerging from a convex lens when a point source is at its focus, and (c) the part of a wavefront from a distant star that reaches Earth.
Steps only
A point source makes spherical wavefronts; a parallel beam makes a plane wavefront. A distant star's wavefront is nearly flat over Earth.
Answer
(a) Spherical; (b) plane; (c) approximately plane.
Question 3
(a) The refractive index of glass is 1.5. Find the speed of light in glass. Use 3.0×10⁸ m/s for its speed in vacuum. (b) Is the speed independent of colour? If not, which travels more slowly in a glass prism, red or violet light?
Steps only
v=c/n=(3.0×10⁸)/1.5=2.0×10⁸ m/s. Violet has a higher refractive index than red, so it travels more slowly.
Answer
(a) 2.0×10⁸ m/s. (b) Violet light.
Question 4
In Young's double-slit experiment, the slit separation is 0.28 mm and the screen is 1.4 m away. The fourth bright fringe is 1.2 cm from the central bright fringe. Find the wavelength of light.
Steps only
λ=yd/(mD)=(0.012)(2.8×10⁻⁴)/(4×1.4)=6.0×10⁻⁷ m.
Answer
600 nm.
Question 5
In Young's double-slit experiment with monochromatic light of wavelength λ, the intensity at a point whose path difference is λ is K. What is the intensity at a point whose path difference is λ/3?
Steps only
For Δ=λ, I_max=K. For Δ=λ/3, φ=2π/3, so I=K cos²(φ/2)=K cos²(π/3)=K/4.
Answer
K/4.
Question 6
Light of wavelengths 650 nm and 520 nm is used in a Young's double-slit experiment. (a) Find the distance of the third bright fringe from the central maximum for 650 nm light. (b) Find the least distance from the centre where bright fringes from both wavelengths coincide.
Steps only
y₃(650)=3(650 nm)D/d=1.95×10⁻⁶(D/d) m. Coincidence needs 650m₁=520m₂; least solution is m₁=4,m₂=5, so y_common=2.60×10⁻⁶(D/d) m.
Answer
The question omits D and d, so only the expressions can be found: third 650 nm fringe 1.95×10⁻⁶(D/d) m; first common bright fringe 2.60×10⁻⁶(D/d) m.