A water tank has a real depth of 16.0\text{ cm}. If the refractive index of water relative… — JAMB UTME

A water tank has a real depth of $16.0\text{ cm}$ . If the refractive index of water relative to air is $\frac{4}{3}$ , what is the apparent depth of the tank in centimetres when viewed normally from above?

Answer: 12 cm

Answer

The apparent depth of the water tank is

12.0\text{ cm}

When light passes from water to air, refraction causes the apparent depth to be smaller than the real depth by a factor equal to the refractive index

n

. Substituting a real depth of

16.0\text{ cm}

and

n = \frac{4}{3}

into

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

yields

12.0\text{ cm}

Step-by-Step Solution

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

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

Refraction at a plane boundary causes an object immersed in a denser medium to appear closer to the surface when viewed from a rarer medium.

Rearrange the equation to isolate Apparent Depth.

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

The unknown quantity requested by the question is the apparent depth.

Substitute the known numerical values into the equation.

\text{Apparent Depth} = \frac{16.0}{\frac{4}{3}} = 16.0 \times \frac{3}{4} = 12.0\text{ cm}

Dividing

16.0

\frac{4}{3}

gives

12.0

Key Concept

Real and Apparent Depth in Light Refraction

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