Question

A swimming pool appears to be raised by \[6\,{\text{m}}\] when viewed normally. What is the refractive index of water if the actual depth of the swimming pool is \[24\,{\text{m}}\]?
A. 1.44
B. 1.33
C. 1.56
D. 1.76

Answer 1

Hint: Calculate the apparent depth of the swimming pool using the formula relating real depth and raised depth. Then use the formula of refractive index of a medium which is in terms of the actual depth and apparent depth.

Formula used:
The apparent depth of an object in a medium is equal to the subtraction of the real (actual) depth of the object and the raised depth of the object when viewed normally.
\[{\text{Apparent depth}} = \left( {{\text{Real depth}}} \right) - \left( {{\text{Raised depth}}} \right)\] …… (1)
The refractive index \[\mu \] of a medium is given by
\[\mu = \dfrac{{{\text{Real depth}}}}{{{\text{Apparent depth}}}}\] …… (2)

Complete step by step answer:
The actual depth of an object is the depth of the object from the surface measured with a real ruler or any other measuring equipment.
The apparent depth of an object in a denser medium is the depth of the object when seen from a rarer medium.
The value of the apparent depth of an object is always less than the real depth of the object.
The actual depth of the swimming pool is \[24\,{\text{m}}\] and it appears to be raised by \[6\,{\text{m}}\] when viewed normally.
Calculate the apparent depth of the swimming pool.
Substitute \[24\,{\text{m}}\] for \[{\text{Real depth}}\] and \[6\,{\text{m}}\] for \[{\text{Raised depth}}\] in equation (1).
\[{\text{Apparent depth}} = \left( {24\,{\text{m}}} \right) - \left( {6\,{\text{m}}} \right)\]
\[ \Rightarrow {\text{Apparent depth}} = 18\,{\text{m}}\]

Hence, the apparent depth of the swimming pool when viewed normally is \[18\,{\text{m}}\].
Now, calculate the refractive index of the water.
Substitute \[24\,{\text{m}}\] for \[{\text{Real depth}}\] and \[18\,{\text{m}}\] for \[{\text{Apparent depth}}\] in equation (2).
\[\mu = \dfrac{{24\,{\text{m}}}}{{18\,{\text{m}}}}\]
\[ \Rightarrow \mu = 1.33\]
Therefore, the refractive index of the water is \[1.33\].

So, the correct answer is “Option B”.

Note:
The apparent depth of the swimming pool is less than the actual depth because the light undergoes refraction at the water surface boundary (air-water interface).