Chapter Questions
A boy makes a pinhole camera out of a cardboard box with the dimensions $10.0 \mathrm{~cm} \times$ $10.0 \mathrm{~cm} \times 16.0 \mathrm{~cm} .$ A pinhole is located in one end, and a film $8.0 \mathrm{~cm} \times 8.0 \mathrm{~cm}$ is placed in the other end. How far away from a tree $25.0 \mathrm{~m}$ high should the boy place his camera if the image of the tree is to be $6.0 \mathrm{~cm}$ high on the film? Ans. $66.7 \mathrm{~m}$
A physics student wishes to repeat Fizeau's experiment for measuring the speed of light. If he uses a toothed wheel containing 1440 teeth and his distant mirror is located in a laboratory window across the college campus $412.60 \mathrm{~m}$ away, how fast must his wheel be rotated if the returning light pulses show the first maximum intensity?
If the mirror $R$ in Foucault's experiment were to rotate at 12,000 rev/min, find $(a)$ the rotational speed of the mirror $R$ in revolutions per second and $(b)$ the rotational speed of the sweeping beam $R M_{1}$ in radians per second. Find the time it takes the light to traverse the path (c) $R M_{1} R$ and $(d) R M_{2} R .$ What is the observed slit deflection $(e) E E_{1}$, and $(f) E E_{2}$ ? Assume the distances $R M_{1}=R M_{2}=6.0 \mathrm{~m}, R S=R E=6.0 \mathrm{~m}$, the
If the refractive index for a piece of optical glass is $1.5250$, calculate the speed of light in the glass.
Calculate the difference between the speed of light in kilometers per second in a vacuum and the speed of light in air if the refractive index of air is $1.0002340 .$ Use velocity values to seven significant figures.
If the moon's distance from the earth is $3.840 \times 10^{5} \mathrm{~km}$, how long will it take microwaves to travel from the earth to the moon and back again
How long does it take light from the sun to reach the earth? Assume the earth's distance from the sun to be $1.50 \times 10^{8} \mathrm{~km} .$
A beam of light passes through a block of glass $10.0 \mathrm{~cm}$ thick, then through water for a distance of $30.5 \mathrm{~cm}$, and finally through another block of glass $5.0 \mathrm{~cm}$ thick. If the refractive index of both pieces of glass is $1.5250$ and of water is $1.3330$, find the total optical path.
A water tank is $62.0 \mathrm{~cm}$ long inside and has glass ends which are each $2.50 \mathrm{~cm}$ thick. If the refractive index of water is $1.3330$ and of glass is $1.6240$, find the overall optical path.
A beam of light passes through $285.60 \mathrm{~cm}$ of water of index $1.3330$, then through $15.40 \mathrm{~cm}$ of glass of index $1.6360$, and finally through $174.20 \mathrm{~cm}$ of oil of index $1.3870 .$ Find to three significant figures $(a)$ each of the separate optical paths and $(b)$ the total optical path.
A ray of light in air is incident on the polished surface of a block of glass at an angle of $10^{\circ} .$ (a) If the refractive index of the glass is $1.5258$, find the angle of refraction to four significant figures. (b) Assuming the sines of the angles in Snell's law can be replaced by the angles themselves, what would be the angle of refraction? (c) Find the percentage error.
Find the answers to Prob. $1.11$, if the angle of incidence is $45.0^{\circ}$ and the refractive index is $1.4265 .$
A ray of light in air is incident at an angle of $54.0^{\circ}$ on the smooth surface of a piece of glass. (a) If the refractive index is 1.5152, find the angle of refraction to four significant figures. (b) Find the angle of refraction graphically.
A straight hollow pipe exactly $1.250 \mathrm{~m}$ long, with glass plates $8.50 \mathrm{~mm}$ thick to close the two ends, is thoroughly evacuated. $(a)$ If the glass plates have a refractive index of $1.5250$, find the overall optical path between the two outer glass surfaces. (b) By how much is the optical path increased if the pipe is filled with water of refractive index 1.33300. Give answers to five significant figures.
Referring to Fig. 1L, the distance $x=6.0 \mathrm{~cm}, h=12.0 \mathrm{~cm}, h=15.0 \mathrm{~cm}, n=1.3330$, and $n^{\prime}=1.5250$. Find $\phi^{\prime}, \phi, d, d^{\prime}, p$, and $\Delta$, to three significant figures.
Solve Prob. 1.15 graphically.
In studying the refraction of light Kepler arrived at a refraction formula$$\phi=\frac{\phi^{\prime}}{1-k \sec \phi^{\prime}} \quad \text { where } \quad k=\frac{n^{\prime}-1}{n^{\prime}}$$$n^{\prime}$ being the relative index of refraction. Calculate the angle of incidence $\phi$ for a piece of glass for which $n^{\prime}=1.7320$ and the angle of refraction $\phi^{\prime}=32.0^{\circ}$ according to(a) Kepler's formula and $(b)$ Snell's law. Note that sec $\phi^{\prime}=1 /\left(\cos \phi^{\prime}\right)$.
White light is incident at an angle of $55.0^{\circ}$ on the polished surface of a piece of glass. If the refractive indices for red $C$ light and blue $F$ light are $n_{c}=1.53828$, and $n_{F}=$ $1.54735$, respectively, what is the angular dispersion between these two colors? (a) Find the two angles to five significant figures and (b) the dispersion to three significant(b) $0.2110^{\circ}$figures.
A piece of dense flint glass is to be made into a prism. If the refractive indices for red, yellow, and blue light are specified as $n_{c}=1.64357, n_{\mathrm{D}}=1.64900$, and $n_{F}=1.66270$, find $($ a) the dispersive power and $(b)$ the dispersion constant for this glass.
A block of spectacle crown glass is to be made into a lens. The refractive indices furnished by the glass manufacturer are specified as $n_{\mathrm{C}}=1.52042, n_{\mathrm{D}}=1.52300$, and $n_{\mathrm{F}}=1.52933 .$ Determine the value of $(a)$ the dispersion constant and $(b)$ the dispersive power.
A piece of extra dense flint glass is to be made into a prism. The refractive indices furnished by the glass manufacturer are those given in Table 1A. Find the value of(a) the dispersive power and ( $b$ ) the dispersion constant.
Two plane mirrors are inclined to each other at an angle $\alpha$. Applying the law of reflection show that any ray whose plane of incidence is perpendicular to the line of intersection of the two mirrors is deviated by two reflections by an angle $\delta$ which is independent of the angle of incidence. Express this deviation in terms of $\alpha$.
An ellipsoidal mirror has a major axis of $10.0 \mathrm{~cm}$, a minor axis of $8.0 \mathrm{~cm}$, and foci $6.0 \mathrm{~cm}$ apart. If there is a point source of light at one focus $Q$, there are only two rays of light that pass through the point $C$, midway between $B$ and $Q^{\prime}$, as can be drawn in Fig. 1J. Draw such an ellipse and graphically determine whether these two paths $Q B C$ and $Q D C$ are maxima, minima, or stationary.
A ray of light in air enters the center of one face of a prism at an angle making $55.0^{\circ}$ with the normal. Traveling through the glass, the ray is again refracted into the air beyond. Assume the angle between the two prism faces to be $60.0^{\circ}$ and the glass to have a refractive index of $1.650 .$ Find the deviation of the ray $(a)$ at the first surface and (b) the second surface, Find the total deviation (c) by calculation and $(d)$ graphically.
One end of a glass rod is ground and polished to the shape of a hemisphere with a diameter of $10.0 \mathrm{~cm}$. Five parallel rays of light $2.0 \mathrm{~cm}$ apart and in the same plane areincident on this curved end, with one ray traversing the center of the hemisphere parallel to the rod axis. If the refractive index is $1.5360$, calculate the distances from the front surface to the point where the refracted rays cross the axis.
Crystals of clear strontium titanate are made into semiprecious gems. The refractive indices for different colors of light are as follows:$$\begin{array}{lllll}\hline & \text { Red } & \text { Yellow } & \text { Blue } & \text { Violet } \\\hline \lambda, \mathrm{A} & 6563 & 5892 & 4861 & 4340 \\n & 2.37287 & 2.41208 & 2.49242 & 2.57168 \\\hline\end{array}$$Calculate the value of $(a)$ the dispersion constant and $(b)$ the dispersive power. Plot a graph of the wavelength $\lambda$ against the refractive index $n .$ Use the blue, yellow, and red indices.