Question

A monochromatic light passes through a glass slab $(\mu =\frac{3}{2})$ a thickness $90cm$ in time $t_1$. If it takes $t_2$ to travel the same distance through water $(\mu =\frac{4}{3})$. The value of $(t_1-t_2)$ is :

• A. $5\times {10}^{-8}s$
• B. $5\times {10}^{-10}s$
• C. $2.5\times {10}^{-10}s$
• D. $2.5\times {10}^{-8}s$

Answer 1

Answer: (B)

$5\times {10}^{-10}s$

$C\to$ Speed of light in vacuum

$V\to$ Speed of light in medium

Refractive Index,

$\mu =C/V$

$time=distance/speed$

${\mu }_1=3/2\left(Glass\right)$

$V_1=\frac{C_1}{{\mu }_1}=\frac{3\times {10}^8}{3/2}=2\times {10}^{8}m/s$

$d=90cm=0.9m$

$t_1=d/V_1=0.9m/2\times {10}^{8}m/s$

$t_1=0.45\times {10}^{-8}s$

${\mu }_2=4/3\left(water\right)$

$V_2=\frac{C_1}{{\mu }_2}=\frac{3\times {10}^{8}m/s}{4/3}=2.25\times {10}^{8}m/s$

$d=90cm=0.9m$

$t_2=\frac{d}{v_2}=\frac{0.9}{0.25\times {10}^{8}m/s}$

$t_2=0.4\times {10}^{-8}s$

$t_1-t_2=0.45\times {10}^{-8}s-0.40\times {10}^{-8}=0.05\times {10}^{-8}s$

$t_1-t_2=5\times {10}^{-10}s$