A swimming pool has an apparent depth of 1.8\text{ m} when viewed vertically from directly… — JAMB UTME

A swimming pool has an apparent depth of $1.8\text{ m}$ when viewed vertically from directly above. If the refractive index of water relative to air is $\frac{4}{3}$ , what is the real depth of the pool in meters?

Cevap: 2.4 m

Cevap

The real depth of the pool is

2.4\text{ m}

The refractive index

n

of a medium is defined as the ratio of the real depth to the apparent depth (

n = \frac{\text{Real Depth}}{\text{Apparent Depth}}

). Multiplying the observed apparent depth of

1.8\text{ m}

by the refractive index

\frac{4}{3}

gives the true real depth of

2.4\text{ m}

Adım Adım Çözüm

Identify the relationship between refractive index, real depth, and apparent depth.

Refractive index

n = \frac{\text{Real Depth}}{\text{Apparent Depth}}

Light bending at the boundary causes an object submerged in a denser medium to appear closer to the surface.

Rearrange the equation to make Real Depth the subject.

\text{Real Depth} = n \times \text{Apparent Depth}.

To calculate the true depth from the observed apparent depth and the optical density of water.

Substitute the given values into the formula.

\text{Real Depth} = \frac{4}{3} \times 1.8\text{ m} = 2.4\text{ m}.

Multiplying the apparent depth by the refractive index yields the actual physical depth.

Anahtar Kavram

Refraction of Light and Real/Apparent Depth

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