Question

You are looking at the rim from the vertical side to see the opposite edge at the bottom of a $16cm$ high and $8cm$ diameter vessel. A friend fills it with a liquid of refractive index $\mu$, so that a coin placed at the center becomes visible. What is the value of $\mu$?

• A. $1.34$
• B. $1.6$
• C. $1.73$
• D. $1.84$

Answer 1

The correct option is D $1.84$

Let the angle of incidence of light be $i$.

Then $sini=\frac{8}{\sqrt{{16}^2+8^2}}=\sqrt{\frac{1}{5}}$

Let the angle of refraction be $r$

.

Thus $sinr=\frac{4}{\sqrt{{16}^2+4^2}}$

$=\sqrt{\frac{1}{17}}$

From snell's law

$sini=\mu sinr$

$⟹\mu =\sqrt{\frac{17}{5}}=1.84$