A pool of water appears to be 1.00m deep when viewed vertically from above. What is the actual depth of the pool? [Refractive index of water = 1.33]

1. Analyze the question

We are given the apparent depth of a pool of water (how deep it looks) and the refractive index of water. We need to calculate the actual depth (the real physical depth of the pool).

2. Explain the concept

When light travels from a denser medium (water) to a rarer medium (air), it bends away from the normal. This causes objects submerged in water to appear shallower than they actually are. This phenomenon is described by the formula for Refractive Index ($n$):

Where:

• $n$ = Refractive index of the medium (water)
• Actual Depth = The real depth of the pool
• Apparent Depth = The depth as perceived by an observer

3. Show the solution

Given:

• Apparent Depth = $1.00\,\text{m}$
• Refractive Index ($n$) = $1.33$

Formula:

Rearranging to find Actual Depth:

Calculation:

4. Identify the answer

Comparing our result to the options provided, the correct value is $1.330\,\text{m}$. This matches option D.

5. Tip

When dealing with refraction problems, always remember: "Real is greater than Apparent." If you are looking at an object in water, the actual depth will always be greater than the apparent depth. If your calculation gives you a number smaller than the apparent depth, you likely swapped the numerator and denominator in your formula!