Question

in a vessel of depth H, upto what height a liquid of refractive index 3/2 should be filled so that the vessel appears half filled as viewed from the top?​

Answer 1

Given :

➳ Depth of vessel = H cm

➳ RI of liquid = 3/2

To Find :

➔ Upto what height a liquid should be filled so that the vessel appears half filled as viewed from the top.

Concept :

⇒ Let it be filled to height x cm, Then the part not in water will be (H - x) cm.

⇒ So the apparent depth of the filled portion must be (H - x) cm.

✴ Refractive index of medium in terms of apparent depth and real depth is given by

$\bigstar\:\underline{\boxed{\bf{RI=\dfrac{Real\:depth}{Apparent\:depth}}}}$

Calculation :

$:\implies\sf\:\dfrac{3}{2}=\dfrac{x}{H-x}$

$:\implies\sf\:3(H-x)=2x$

$:\implies\sf\:3H-3x=2x$

$:\implies\sf\:3H=5x$

$:\implies\underline{\boxed{\bf{x=\dfrac{3H}{5}\:cm}}}$