Question

Taking the speed of light in vacuum to be 3.000 x 10^8 m/s, find the speed of light in: a. air b. diamond c. crown glass d. water Data: nair =1.0003; ndiamond = 2.420; nwater = 1.340 ncrown glass = 1.500

Answer 1

Explanation:

The speed of light in vacuum is, c = 3 × 10⁸ m/s

We have to find the speed of light :

(a) In air :

$n_1_{air}=1.0003$

The equation of refractive index is given as :

$n_1=\dfrac{c}{v_1}$

$v_1=\dfrac{c}{n_1}$

$v_1=\dfrac{3\times 10^8\ m/s}{1.0003}$

$v_1=299910026.9\ m/s$

$v_1=2.99\times 10^8\ m/s$

(b) In diamond :

$n_2_{diamond}=2.42$

The equation of refractive index is given as :

$n_2=\dfrac{c}{v_2}$

$v_2=\dfrac{c}{n_2}$

$v_2=\dfrac{3\times 10^8\ m/s}{2.42}$

$v_2=123966942.1\ m/s$

$v_2=1.23\times 10^8\ m/s$

(c) In crown glass :

$n_3_{glass}=1.5$

The equation of refractive index is given as :

$n_3=\dfrac{c}{v_3}$

$v_3=\dfrac{c}{n_3}$

$v_3=\dfrac{3\times 10^8\ m/s}{1.5}$

$v_3=200000000\ m/s$

$v_3=2\times 10^8\ m/s$

(4) In water :

$n_4_{glass}=1.34$

The equation of refractive index is given as :

$n_4=\dfrac{c}{v_4}$

$v_4=\dfrac{c}{n_4}$

$v_4=\dfrac{3\times 10^8\ m/s}{1.34}$

$v_4=223880597.01\ m/s$

$v_4=2.23\times 10^8\ m/s$

Hence, this is the required solution.