Exercises of theme 3

 Problem 1

The speed of light on the ice is \(2.29x10^{8^{ }}\)m/s . what is the refractive index on the ice?
For which we use the following formula.
\(n=\frac{c}{v}\)
we substitute knowing that the speed of light is \(3x10^8\)m/s, would be as follows.
\(n=\frac{3x10_{\frac{m}{s}}^8}{2.29x10_{\frac{m}{s}}^8}\)
 What is equal to \(1.03x10^8\)m/s

Problem 2

What is the speed of light in ethyl alcohol.
For which we use the following formula  \(v=\frac{c}{n}\)
n is the value of ethyl alcohol \(\left(1.36\right)\) and we substitute the formula
\(v=\frac{3x10_{\frac{m}{s}}^8}{1.36}\ =\ 2.20x10^8\)m/s

Problem 3 

The nearest star that is not the sun is 4.2 light years, how far is it in meters?
For which we use the following formula  \(c=\frac{d}{t}\)
In this case as the formula is dividing, goes to multiplying
\(d=\left(3x10_{\frac{m}{s}}^8\right)\left(3600\right)\left(24\right)\left(365\right)\left(4.2\right)\)
What gives  \(=3.97x10^{16}\ m\)

Problem 4

The speed of light in a certain substance is 88% of its value in water. Which is the index of refraction in that substance?
For which we use the following formula  \(n_m=\frac{c}{v_m}\)  , we know  that \(\frac{v_m}{V\left(H_2O\right)}=0.88\)  and as this formula is dividing happens to multiplying.
\(n_m=\frac{c}{\left(0.88\right)\left(0.75\right)}=\frac{1}{\left(0.88\right)\left(0.75\right)}=1.51\)

Problem 5   

A swimmer lights a lamp up from below the water at an angle of 38.5 with respect to the vertical, at what angle does the water leave the light?