A container holds a layer of water of depth 16.0\text{ cm}. An immiscible layer of oil of … — JAMB UTME

A container holds a layer of water of depth $16.0\text{ cm}$ . An immiscible layer of oil of refractive index $1.20$ and thickness $6.0\text{ cm}$ floats on top of the water. If the refractive index of water is $1.33$ (or $\frac{4}{3}$ ), what is the total apparent depth, in centimeters, of a small object resting at the bottom of the container when viewed normally from directly above?

Cevap: 17 cm

Cevap

The total apparent depth of the object when viewed normally from directly above is

17.0\text{ cm}

When an object at the bottom of a container is viewed normally through multiple transparent media, the overall apparent depth is the sum of the apparent depths produced by each medium individually (

d_{\text{app}} = \sum \frac{d_i}{n_i}

). Substituting the given values gives

\frac{16.0}{4/3} + \frac{6.0}{1.20} = 12.0\text{ cm} + 5.0\text{ cm} = 17.0\text{ cm}

Adım Adım Çözüm

Calculate the apparent depth of the water layer.

Apparent depth of water =

12.0\text{ cm}

Apparent depth in a single medium is given by the real depth divided by its refractive index (

d_{\text{app}} = d / n

). For water,

\frac{16.0}{4/3} = 12.0\text{ cm}

Calculate the apparent depth of the oil layer.

Apparent depth of oil =

5.0\text{ cm}

Using

d_{\text{app}} = d / n

for the oil layer,

\frac{6.0}{1.20} = 5.0\text{ cm}

Sum the apparent depths of both media.

Total apparent depth =

17.0\text{ cm}

For multiple parallel transparent layers, the total apparent depth is the sum of the apparent depths of each individual layer.

Anahtar Kavram

Apparent depth in composite media layers

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