Chapter 25

Top $1\text{.}\text{715 m}$ from floor, bottom $0\text{.}\text{825 m}$ from floor. Height of mirror is $0\text{.}\text{890 m}$, or precisely one-half the height of the person.

$2\text{.}\text{25}\times {\text{10}}^8\text{m/s}$ in water

$2\text{.}\text{04}\times {\text{10}}^8\text{m/s}$ in glycerine

$1\text{.}\text{490}$, polystyrene

$1\text{.}\text{28 s}$

$\mathrm{1.03\; ns}$

$n=1\text{.}\text{46}$, fused quartz

(a) 0.898

(b) Can’t have $n<1\text{.}\text{00}$ since this would imply a speed greater than $c$.

(c) Refracted angle is too big relative to the angle of incidence.

(a) $\frac{c}{5\text{.}\text{00}}$

(b) Speed of light too slow, since index is much greater than that of diamond.

(c) Angle of refraction is unreasonable relative to the angle of incidence.

$\text{66}\text{.}\mathrm{3º}$

$>1\text{.}\text{414}$

1.50, benzene

$\text{46}\text{.}\mathrm{5º}\text{, red; 46}\text{.}\mathrm{0º}\text{, violet}$

(a) $0\text{.}\text{043º}$

(b) $1\text{.}\text{33 m}$

$\text{71.3º}$

$\text{53.5º}\text{, red;}$ $\text{55.2º}\text{, violet}$

$\text{5.00 to 12.5 D}$

$-\mathrm{0.222\; m}$

(a) 3.43 m

(b) 0.800 by 1.20 m

(a) $-1\text{.}\text{35 m}$ (on the object side of the lens).

(b) $+\text{10}\text{.}0$

(c) 5.00 cm

44.4 cm

(a) 6.60 cm

(b) –0.500

(a) $+7\text{.}\text{50 cm}$

(b) $\text{13}\text{.}\text{3 D}$

(c) Much greater

(a) +6.67

(b) +20.0

(c) The magnification increases without limit (to infinity) as the object distance increases to the limit of the focal distance.

$-0\text{.}\text{933 mm}$

+0.667 m

(a) $\mathrm{–1.5}\times {10}^{\mathrm{–2}}\text{m}$

(b)$\mathrm{–66.7\; D}$

+0.360 m (concave)

(a) +0.111

(b) -0.334 cm (behind “mirror”)

(c) 0.752cm

$\text{6.82 k}{\text{W/m}}^2$

(a) $\begin{array}{l}{v}_{610}=\frac{3.00\times {10}^8}{1.530}\text{m/s, }{v}_{410}=\frac{3.00\times {10}^8}{1.514}\text{m/s}\\ \text{3}\text{.00}\times {\text{10}}^8\left(\frac{1}{1.514}-\frac{1}{1.530}\right)\text{m/s}=2.07\times {10}^6\text{ m/s}\end{array}$

(b) No.

(c) No.

(d) Yes.

(c)

(c)

(a)

Since light bends toward the normal upon entering a medium with a higher index of refraction, the upper path is a more accurate representation of a light ray moving from A to B.

First, measure the angle of incidence and the angle of refraction for light entering the plastic from air. Since the two angles can be measured and the index of refraction of air is known, the student can solve for the index of refraction of the plastic.

Next, measure the angle of incidence and the angle of refraction for light entering the gas from the plastic. Since the two angles can be measured and the index of refraction of the plastic is known, the student can solve for the index of refraction of the gas.

The speed of light in a medium is simply c/n, so the speed of light in water is 2.25 × 10⁸ m/s. From Snell’s law, the angle of incidence is 44°.

(d)

(a)

(a)

(b)