# How much water should be filled in a container 21cm in height, so that it appears half-filled when viewed from the top of the container?

Piyush
8 years ago

Real depth = 21-x
Apparent depth =x (look into the fig.)


x=9
Real depth =12cm
Dev Aggarwal
25 Points
7 years ago
what. even.
the question clearly states that the container must look ‘HALF FILLED’. i mean half filled ffs. the apparent depth must be 21/2 = 10.5.
taking real depth = x
apparent depth (given) = 10.5
we can say
x/10.5 = 4/3
giving x = 14 cm.
Ashish
12 Points
5 years ago
So simple Real -unreal /unreal = refractive index Given real =21 21-x/x=4/3 On calculating We get answe as unreal, x=12 which is required appear viewed from top
Amila
15 Points
5 years ago
Hi,
Let’s say required height of water is “X cm”. Then top of the water surface is located at (21-X) cm distance from top of the container. Once water is filled up to “X cm” height, bottom of the container will be raised(Apparent bottom). Let’s say apparent height of the bottom of the container is “Y cm” from top of the water surface.

Then
real height/ apparent height  = refractive index of water relative to air
X/Y= n
X/Y = 4/3
Y=3X/4
Now  w.r.t the viewer, total height of the container is reduced. And,
new total height(apparent height) of the container = (21-X) + Y
And to view as half filled, Y= [(21-X) + Y]/2
2Y=(21-X) + Y
Y= 21-X
3X/4= 21-X
X= 12 cm.
Therefore required height is 12 cm
Thanks
Yash Chourasiya
3 years ago
Dear Student

Let it be filled to height h cm. Then the part not in water is (21-h) cm.
So the apparent depth of the filled portion must be (21-h) cm.
realdepth​/apparent depth = refractiveindexofwater
h / (21−h) = 1.33
h = 12cm