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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?

Ishaan Gautam , 10 Years ago

Grade 12th pass

5 Answers

Piyush

Last Activity: 9 Years ago

$\frac{Real depth}{Apparent depth} = Refractive index$
Real depth = 21-x
Apparent depth =x (look into the fig.)

$\frac{21-x}{x} = \frac{4}{3}$
x=9
Real depth =12cm

Dev Aggarwal

Last Activity: 8 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

Last Activity: 6 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

Last Activity: 6 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

Last Activity: 4 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

I hope this answer will help you.
Thanks & Regards
Yash Chourasiya