A column of liquid is 10 cm high.Viewed from above the liquid has an apparent depth of 6.77 cm.If the refractive index of the liquid is 1.33 at the top and increases uniformly to the bottom,then what is the refractive index at the bottom of the liquid?
A)1.96
B)2.95
C)1.48
D)1.62
E)None of these is correct.

Question

Quizplus · Accepted Answer

Using the formula for apparent depth, we can write:
Real depth = Apparent depth / Refractive index
Let the real depth of the liquid be h.
h = 6.77 / 1.33
h = 5.08 cm
Now, let's consider a small element of height dh at a depth h from the top. The refractive index at this depth can be written as:
n(h) = 1.33 + k.h
where k is a constant.
We know that at the top (h = 0), n = 1.33. Plugging this in the above equation, we get:
1.33 = 1.33 + k.0
k = 0
So, the refractive index equation becomes:
n(h) = 1.33
This means that the refractive index is constant throughout the liquid, and hence equal to 1.33.

A Column of Liquid Is 10 Cm High