Question

Velocity of light in glass is $2\times {10}^{8}m{s}^{-1}$ and that in air is $3\times {10}^{8}m{s}^{-1}$. By how much would an ink dot appear to be raised, when covered by a glass plate 6.0 cm thick?

• A. $2.0cm.$
• B. $6.0cm.$
• C. $4.0cm.$
• D. none of the above

Answer 1

Answer: (A)

$2.0cm.$

Here, Velocity of light in air,

$C=3\times {10}^{8}m{s}^{-1}$

Velocity of light in glass,

$v=2\times {10}^{8}m{s}^{-1}$

Therefore, refractive index of glass w.r.t air,

$\mu =\frac{c}{v}=\frac{3\times {10}^8}{2\times {10}^8}=1.5$

Normal shift in the position of the ink dot,

$d=t(1-\frac{1}{\mu })$

Here the thickness of the glass plater, $t=6.0cm$

$\therefore d=6.0(1-\frac{1}{1.5})=\frac{6\times 0.5}{1.5}=2.0cm.$