Two clear but non-mixing liquids each of depth 15 cm are placed together in a glass container.The liquids have refractive indices of 1.75 and 1.33.What is the apparent depth of the combination when viewed from above?
A)19.8 cm
B)23.1 cm
C)17.7 cm
D)9.9 cm
E)None of these is correct.

Question

Quizplus · Accepted Answer

To find the apparent depth, we use the formula:

Apparent depth = Actual depth / Refractive index

Let the actual depths of the two liquids be h1 and h2, respectively, where h1 + h2 = 15 cm (since each liquid has a depth of 15 cm).

Then, the apparent depth of the first liquid when viewed from above is:

h1' = h1 / n1

Similarly, the apparent depth of the second liquid is:

h2' = h2 / n2

When viewed from above, the apparent depth of the combination is the sum of the two apparent depths:

h' = h1' + h2'

Substituting the values, we get:

h' = (h1 / n1) + (h2 / n2)

h' = (15 / 1.75) + (15 / 1.33)

h' = 8.57 + 11.28

h' = 19.85 cm (approx)

Therefore, the apparent depth of the combination when viewed from above is 19.8 cm(approx).

Two Clear but Non-Mixing Liquids Each of Depth 15 Cm