Question

A mark at the bottom of the liquid appears to rise by \(0.2 \mathrm{~m}\), If depth of the liquid is \(2.0 \mathrm{~m}\) then refractive index of the liquid is (A) \(1.80\) (B) \(1.60\) (C) \(1.33\) (D) \(1.11\)

Short answer

The refractive index of the liquid is (D) \(1.11\).

Step-by-step solution

Understand the given information

We are given that the apparent rise in depth is 0.2m, and the actual depth of the liquid is 2.0m. We need to find the refractive index of the liquid.

Formula for apparent depth and actual depth

The relationship between the apparent depth (d') and the actual depth (d) is given by the formula: \(d' = \frac{d}{n}\) where n is the refractive index of the liquid.

Calculate the apparent depth using the given information

We are given that the apparent rise in depth is 0.2m. Therefore, the apparent depth (d') can be calculated as: \(d' = 2.0m - 0.2m = 1.8m\)

Solve for the refractive index

Now that we have the apparent depth (d') and actual depth (d), we can solve for the refractive index (n). Re-write the formula from step 2: \(n = \frac{d}{d'}\) Plugging the values for the actual depth (d=2.0m) and the apparent depth (d'=1.8m): \(n = \frac{2.0m}{1.8m} = \frac{20}{18}\)

Simplify the refractive index

Simplify the refractive index to get the final answer: \(n = \frac{20}{18} = 1.11\)

Compare the calculated value with the given options

Comparing the calculated refractive index (n=1.11) with the given options, we find that the correct answer is: (D) \(1.11\)