Question

The refractive index of denser medium with respect to rarer medium is 1.125. The difference between the velocities of light in the two media is $0.25\times {10}^8$ m/s. The velocities of light in the two media are (c $=3\times {10}^8$ m/s):

• A. $2.0\times {10}^8$ m/s; $2.25\times {10}^8$ m/s
• B. $2\times {10}^8$ m/s; $2.5\times {10}^8$ m/s
• C. $2.5\times {10}^8$ m/s; $3\times {10}^8$ m/s
• D. $2\times {10}^8$ m/s; $3\times {10}^8$ m/s

Answer 1

The correct option is A $2.0\times {10}^8$ m/s; $2.25\times {10}^8$ m/s

Velocity of light in denser medium $V_r$ $=\frac{\nu }{{\mu }_2}$
$V_r$ $=\frac{3\times {10}^8}{{\mu }_2}$
Velocity of light in rarer medium $V_d$ $=\frac{\nu }{{\mu }_1}$
$V_d$ $=\frac{3\times {10}^8}{{\mu }_1}$

Given, $\frac{{\mu }_2}{{\mu }_1}=1.125$

${\mu }_2=1.125{\mu }_1$

Given, $V_r-V_d=0.25\times {10}^8$

$⟹$ $\frac{3\times {10}^8}{{\mu }_1}-\frac{3\times {10}^8}{{\mu }_2}=0.25\times {10}^8$

So, $V_d=2\times {10}^{8}m/s$ and $V_r=2.25\times {10}^{8}m/s$