Question

Refractive index of glass relative water is 1.2 and that of water relative to a medium X is 10/11. If speed of ray of light in glass is $1.875\times {10}^{8}m/s$ then speed in the medium X is

• A. $2.04\times {10}^8$
• B. $3.00\times {10}^8$
• C. $1.875\times {10}^8$
• D. all of these

Answer 1

The correct option is A $2.04\times {10}^8$

$\frac{{\mu }_g}{{\mu }_w}=1.2$

$\frac{{\mu }_w}{{\mu }_x}=\frac{10}{11}$

Speed of ray of light in glass = $1.875\times {10}^8\text{m/s}$

From the given data,

$\frac{{\mu }_g}{{\mu }_w}\times \frac{{\mu }_w}{{\mu }_x}=1.2\times \frac{10}{11}$

$\Rightarrow \frac{{\mu }_g}{{\mu }_x}=\frac{12}{11}$

Speed of light in medium is given by the formula

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

$\Rightarrow \frac{v_g}{v_x}=\frac{{\mu }_x}{{\mu }_g}$

Substituting the values,

$\Rightarrow \frac{1.875\times {10}^8\text{m/s}}{v_x}=\frac{11}{12}$

$\Rightarrow v_x=2.04\times {10}^8\text{m/s}$

Speed in medium x is $2.04\times {10}^8\text{m/s}$