A swimming pool is 2.1m deep. If it contains water of refractive index 1.3, calculate the apparent depth of pool

Analyze the question: A pool of real depth 2.1 m is filled with water (n = 1.3). When you look straight down into water, it looks shallower than it really is. We need the apparent depth.

Concept: For near-normal viewing, refractive index is the ratio of real depth to apparent depth:

n = real depth / apparent depth

so

apparent depth = real depth / n

Solution:

Apparent depth = 2.1 / 1.3

= 1.615... m

≈ 1.6 m

Check the options:

• A (3.4 m) and B (2.7 m) are greater than the real depth. This is impossible, because apparent depth in water is always less than real depth.
• D (0.8 m) is too small. It would result from dividing incorrectly or using the wrong ratio.
• C (1.6 m) matches our calculation.

Tip: Water makes objects look shallower, so the apparent depth must always be less than the real depth. Remember "real over apparent equals n". Immediately eliminate any option bigger than the real depth. This will often leave you with only one or two options to check.