a. How long (in ns) does it take light to travel $1.0\mathrm{m}$in vacuum?

b. What distance does light travel in water, glass, and cubic zirconia during the time that it travels $1.0\mathrm{m}$in vacuum?

1. The medium's degree for refraction $n$was described as the proportion

role="math" localid="1649089719687" $n=\frac{c}{v}$ $\left(1\right)$

The maximum speed into vacuum was $c=3.0\times {10}^8\mathrm{m}/\mathrm{s}$and also the light speed inside the media is $v$.

2. The Ray Structure of Light: Light passes at $v=c/n$via neat lines called light ray. The light ray will persist indefinitely except if it interacts with substance, in which case it will reflects, refract, disperse, or be consumed. Light rays are emitted by things. Rays are sent out in every dimensions from every spot on the item. When divergent rays are gathered either by pupil and centered just on retina, the person perceives an item (or a picture). If lens, reflectors, and apertures are bigger over $\approx 1\mathrm{mm}$, ray optics is acceptable.

3. The molecule's maximum pace was equivalent here to proportion of the number path that moves divided by the sum period that goes a certain length:

$v_{\mathrm{avg}}=\frac{d}{\mathrm{\Delta }t}$ $\left(2\right)$

Through air, beam passes the range of:$d=1.0\mathrm{m}$

Water has a reflectivity of:$n_w=1.33$

Glass has a reflectivity of:$n_g=1.50$

Zirconia has a reflectivity of:$n_c=2.16$

In vacuum, its light speed would be:$c=3.0\times {10}^8\mathrm{m}/\mathrm{s}$

a) Formula $\left(2\right)$provides that time required for light to pass the $1.0-m$length through vacuum:

$\mathrm{\Delta }t=\frac{d}{c}$

Put appropriate data:

$\mathrm{\Delta }t=\frac{1.0\mathrm{m}}{3.0\times {10}^8\mathrm{m}/\mathrm{s}}$

$=3.33\times {10}^{-9}\mathrm{s}$

$=\left(3.33\times {10}^{-9}\mathrm{s}\right)\left(\frac{{10}^9\mathrm{ns}}{1\mathrm{s}}\right)$

$=3.3\mathrm{ns}\left(3.33\mathrm{ns}\right)$

$=3.33\times {10}^{-9}\mathrm{s}$

b) The light speed in water is obtained from formula $\left(1\right)$

$v_w=\frac{c}{n_w}$

Put appropriate data:

$v_w=\frac{3.0\times {10}^8\mathrm{m}/\mathrm{s}}{1.33}$

$=2.255\times {10}^8\mathrm{m}/\mathrm{s}$

Formula $\left(2\right)$will be used to measure the position travelled for lights through liquid as $\mathrm{\Delta }t$.

$d_w=v_w\mathrm{\Delta }t$

Put appropriate data:

$d_w=\left(2.255\times {10}^8\mathrm{m}/\mathrm{s}\right)\left(3.3\times {10}^{-9}\mathrm{s}\right)$

$=0.75\mathrm{m}$

$=2.255\times {10}^8\mathrm{m}/\mathrm{s}$

The light speed in glass is obtained from formula$\left(1\right)$

$v_g=\frac{c}{n_g}$

Put appropriate data:

$v_g=\frac{3.0\times {10}^8\mathrm{m}/\mathrm{s}}{1.50}$

$=2.0\times {10}^8\mathrm{m}/\mathrm{s}$

Formula $\left(2\right)$will be used to measure the position travelled for lights through glass as $\mathrm{\Delta }t$.

$d_g=v_g\mathrm{\Delta }t$

Put appropriate data:

$d_g=\left(2.0\times {10}^8\mathrm{m}/\mathrm{s}\right)\left(3.33\times {10}^{-9}\mathrm{s}\right)$

$=0.67\mathrm{m}$

The light speed in cubic zirconia is obtained from formula $\left(1\right)$

$v_c=\frac{c}{n_c}$

Put appropriate data:

$v_c=\frac{3.0\times {10}^8\mathrm{m}/\mathrm{s}}{2.16}$

$=1.389\times {10}^8\mathrm{m}/\mathrm{s}$

Formula $\left(2\right)$ will be used to measure the position travelled for lights through cubic zirconia as $\mathrm{\Delta }t$.

role="math" localid="1649094274035" $d_c=v_c\mathrm{\Delta }t$

Put appropriate data:

$d_c=\left(1.389\times {10}^8\mathrm{m}/\mathrm{s}\right)\left(3.33\times {10}^{-9}\mathrm{s}\right)$

$=0.46\mathrm{m}$