Question

The refractive index of the material of crystal is $1.68$ and that of castor oil is $1.2$. When a ray of light passes from oil to glass, its velocity will change by a factor

• A. $\frac{2}{3}$
• B. $\frac{3}{4}$
• C. $\frac{5}{6}$
• D. $\frac{5}{7}$

Answer 1

Answer: (D)

We know, refractive index of crystal w.r.t. oil,
${\mu }_{co}=\frac{{\mu }_c}{{\mu }_o}=\frac{\text{ speed of light in oil }}{\text{ speed of light in crystal }}$
Where, ${\mu }_c=$ absolute refractive index of crystal w.r.t. vacuum.
and ${\mu }_0=$ absolute refractive index of oil w.r.t. vacuum.
${\mu }_{co}=\frac{1.68}{1.2}=\frac{7}{5}=\frac{\text{ speed in oil }}{\text{ speed in crystal }}$
Fractional change in velocity, when light travel from oil to crystal
$=\frac{\text{ speed in crystal }}{\text{ speed in oil }}=\frac{5}{7}$