Question

A ray of light is incident on a glass-water interface at an angle i, it merges finally parallel to the surface of the water as shown in the figure, the value of ${\mu }_g$ would be:

• A. (4/3) sin i
• B. 1 /sin i
• C. 4/3
• D. 1

Answer 1

The correct option is B

1 /sin i

By applying snell's law

At first surface: (glass to water)

$\frac{sini}{sinr}=\frac{absoluterefractiveindexofwater}{absoluterefractiveindexofglass}=\frac{{\mu }_{\omega }}{{\mu }_g}=\frac{4}{3{\mu }_g}....\left(1\right)$

A second surface: (water to air)
$\frac{sini}{sinr}=\frac{absoluterefractiveindexofair}{absoluterefractiveindexofwater}$
$sinr=\frac{1}{{\mu }_{\omega }}=\frac{3}{4}$ ....(2)

substituting this value in (1)

$4\frac{sini}{3}=\frac{4}{3{\mu }_g}$

$\Rightarrow {\mu }_g=\frac{1}{sini}$