Question

Refractive index of glass is 1.5and that of diamond is 2.4 if velocity of lighting glass is 2.6× 10^8. calculate the velocity of light in diamon​

Answer 1

Given,

Refractive index of glass {n(g)}= 1.5

Refractive index of diamond {n(d)} = 2.4

Velocity of light in glass {v(g)} =

$2.6 \times {10}^{8} \frac{m}{s}$

To find: velocity of light in diamond {v(g)}

$\boxed{first}$

Let's find the speed of light in air.

We know,

$n = \frac{c}{v}$

where, c = speed of light in air.

v = speed of light in any medium.

So,

$= > \: \: n(g) = \frac{c}{v(g)}$

$= > \: \: 1.5 = \frac{c}{2.6 \times {10}^{8} }$

$= > \: \: c = 3.9 \times {10}^{8}$

So, we got speed of light in air =

$3.9 \times {10}^{8} \frac{m}{s}$

$\boxed{second}$

Now, let us find the speed of light in diamond.

$= > \: n(d) = \frac{c}{v(d)}$

$= > \: 2.4 = \frac{3.9 \times {10}^{8} }{v(d)}$

$= > \: v(d) = \frac{3.9 \times {10}^{8} }{2.4}$

$= > \: v(d) = 1.625 \times {10}^{8} \frac{m}{s}$

So , the speed of light in diamond is

$1.625 \times {10}^{8 \frac{m}{s} }$