A vessel of depth 2 h is half filled with a liquid of refractive index 2√2 and the upper half with another liquid of refractive index √2 The liquids are immiscible. The apparent depth of the inner surface of the bottom of vessel will be :

Question

A vessel of depth 2 h is half filled with a liquid of refractive index 2√2 and the upper half with another liquid of refractive index √2 The liquids are immiscible. The apparent depth of the inner surface of the bottom of vessel will be : (A) (h/√2) (B) (3/4)h√2 (C) (h/3√2) (D) (h/2(√2+1))

Tardigrade Admin · Accepted Answer

For near normal incidence, happ=(hactual/((μin)μref.)) ∴ happarent=((h/((2√2)√2))+h/(√2)1)=(3h/2√2)=(3/4)h√2

Q. A vessel of depth $2 h$ is half filled with a liquid of refractive index $22$ and the upper half with another liquid of refractive index $2$ The liquids are immiscible. The apparent depth of the inner surface of the bottom of vessel will be :

$\frac{h}{2}$

$\frac{3}{4} h 2$

$\frac{h}{3 2}$

$\frac{h}{2 ( 2 + 1 )}$

For near normal incidence,
$h_{a pp} = \frac{h _{a c t u a l}}{( \frac{μ _{in}}{μ _{re f .}} )}$
$∴ h_{a pp a re n t} = \frac{\frac{h}{( \frac{2 2}{2} )} + h}{\frac{2}{1}} = \frac{3 h}{2 2} = \frac{3}{4} h 2$

Q. A vessel of depth 2h is half filled with a liquid of refractive index 22​ and the upper half with another liquid of refractive index 2​ The liquids are immiscible. The apparent depth of the inner surface of the bottom of vessel will be :

2​h​

43​h2​

32​h​

2(2​+1)h​