Chapter 23, Problem 27P

To determine

Part (a) To Determine:

The speed of light in (a)Ethyl alcohol.

Answer to Problem 27P

Solution:

The speed of light in (a)Ethyl alcohol is $v_{ethyl-alcohol}=2.21\times {10}^8\text{m/s}$

Explanation of Solution

Given Info:

Speed of light in vacuum $c=3.0\times {10}^8\text{m/s}$

Refractive index of Ethyl alcohol is 1.36

Formula Used:

The refractive index of any medium $n=\frac{c}{v}$

Here, all alphabets are in their usual meanings.

Calculation:

The refractive index of Ethyl alcohol $n_{ethyl-alcohol}=\frac{c}{v_{ethyl-alcohol}}$

$\begin{array}{l}or,v_{ethyl-alcohol}=\frac{c}{n_{ethyl-alcohol}}\\ or,v_{ethyl-alcohol}=\frac{3.0\times {10}^{8}m/s}{1.36}\\ or,v_{ethyl-alcohol}=2.21\times {10}^{8}m/s\end{array}$

To determine

Part (b) To Determine:

The speed of light in (b)Lucite.

Answer to Problem 27P

Solution:

The speed of light in (b)Lucite is $v_{\text{Lucite}}=1.99\times {10}^{8}m/s$

Explanation of Solution

Given Info:

Speed of light in vacuum $c=3.0\times {10}^{8}m/s$

Refractive index of Lucite is 1.51

Formula Used:

The refractive index of any medium $n=\frac{c}{v}$

Here, all alphabets are in their usual meanings.

Calculation:

The refractive index of Lucite $n_{\text{Lucite}}=\frac{c}{v_{\text{Lucite}}}$

$\begin{array}{l}or,v_{\text{Lucite}}=\frac{c}{n_{\text{Lucite}}}\\ or,v_{\text{Lucite}}=\frac{3.0\times {10}^{8}m/s}{1.51}\\ or,v_{\text{Lucite}}=1.99\times {10}^{8}m/s\end{array}$

To determine

Part (c) To Determine:

The speed of light in (c)Crown glass.

Answer to Problem 27P

Solution:

The speed of light in (c)Crown glass is $v_{\text{Crown glass}}=1.97\times {10}^{8}m/s$

Explanation of Solution

Given Info:

Speed of light in vacuum $c=3.0\times {10}^{8}m/s$

Refractive index of Crown glass is 1.52

Formula Used:

The refractive index of any medium $n=\frac{c}{v}$

Here, all alphabets are in their usual meanings.

Calculation:

The refractive index of Crown glass $n_{\text{Crown glass}}=\frac{c}{v_{\text{Crown glass}}}$

$\begin{array}{l}or,v_{\text{Crown glass}}=\frac{c}{n_{\text{Crown glass}}}\\ or,v_{\text{Crown glass}}=\frac{3.0\times {10}^{8}m/s}{1.52}\\ or,v_{\text{Crown glass}}=1.97\times {10}^{8}m/s\end{array}$