Question

12. (5 pts) For the following substances, determine the velocity at which light travels through them and the corresponding index of refraction (n), assuming that the speed of light in a vacuum is 3 x 100 cm/s. Substance V (cm/s) V (m/s) Ice f(Hz) 3.27 x 1014 2. (cm) 700x107 Oil 6.17 x 1014 320x10? Water 4.70 x 1014 480x107 Bromine 5.48 x 1014 330x107 Cubic Zirconia 2.91 x 104 480x102

Answer 1

The speed of light in a material through which it passes will be given by -

v = $\lambda$ f

The index of refraction of a material which will be given by -

n = c / v

where, c = speed of light in a vacuum = 3 x 10¹⁰ cm/s

(i) For substance "Ice", we have

v = [(700 x 10^-7 cm) (3.27 x 10¹⁴ Hz)]

v = 2.28 x 10¹⁰ cm/s

Converting cm/s into m/s :

v = (2.28 x 10¹⁰ cm/s) [(1 m/s) / (100 cm/s)]

v = 2.28 x 10⁸ m/s

We know that, n = c / v = [(3 x 10¹⁰ cm/s) / (2.28 x 10¹⁰ cm/s)]

n = 1.31

(ii) For substance "Oil", we have

v = [(320 x 10^-7 cm) (6.17 x 10¹⁴ Hz)]

v = 1.97 x 10¹⁰ cm/s

Converting cm/s into m/s :

v = (1.97 x 10¹⁰ cm/s) [(1 m/s) / (100 cm/s)]

v = 1.97 x 10⁸ m/s

We know that, n = c / v = [(3 x 10¹⁰ cm/s) / (1.97 x 10¹⁰ cm/s)]

n = 1.52

(iii) For substance "Water", we have

v = [(480 x 10^-7 cm) (4.70 x 10¹⁴ Hz)]

v = 2.25 x 10¹⁰ cm/s

Converting cm/s into m/s :

v = (2.25 x 10¹⁰ cm/s) [(1 m/s) / (100 cm/s)]

v = 2.25 x 10⁸ m/s

We know that, n = c / v = [(3 x 10¹⁰ cm/s) / (2.25 x 10¹⁰ cm/s)]

n = 1.33

(iv) For substance "Bromine", we have

v = [(330 x 10^-7 cm) (5.48 x 10¹⁴ Hz)]

v = 1.80 x 10¹⁰ cm/s

Converting cm/s into m/s :

v = (1.80 x 10¹⁰ cm/s) [(1 m/s) / (100 cm/s)]

v = 1.80 x 10⁸ m/s

We know that, n = c / v = [(3 x 10¹⁰ cm/s) / (1.80 x 10¹⁰ cm/s)]

n = 1.66

(v) For substance "Cubic Zirconia", we have

v = [(480 x 10^-7 cm) (2.91 x 10¹⁴ Hz)]

v = 1.39 x 10¹⁰ cm/s

Converting cm/s into m/s :

v = (1.39 x 10¹⁰ cm/s) [(1 m/s) / (100 cm/s)]

v = 1.39 x 10⁸ m/s

We know that, n = c / v = [(3 x 10¹⁰ cm/s) / (1.39 x 10¹⁰ cm/s)]

n = 2.15