Question

A fish in water sees an object 24 cm above the surface of water. The height of object above the surface of water that will appear to fish is
 A. \[8\;{\rm{cm}}\]
B. \[18\;{\rm{cm}}\]
C. \[24\;{\rm{cm}}\]
D. \[32\;{\rm{cm}}\]

Answer 1

Hint: The given problem is resolved using the formula relating the to the reflection as well as the refractive index. The mathematical relation signifying the height seen by any object with corresponding refractive index of the medium is also taken into consideration.

Complete step by step answer:
The height observed by the fish is, \[H = 24\;{\rm{cm}}\].
Let h be the height of the object above the surface.
Then the formula for the height observed by any object beneath the surface is given as,
\[H = h \times \dfrac{{{\mu _2}}}{{{\mu _1}}}\]
Here, \[{\mu _1}\] and \[{\mu _2}\] are the refractive indices of the medium where the fish resides and object is kept. Since the fish is observed to be in water and the object is kept in the surrounding containing air.
So the value of refractive indices are 4/3 and 1 respectively.

Substituting the values in the relation as,
 \[\begin{array}{l}
H = h \times \dfrac{{{\mu _2}}}{{{\mu _1}}}\\
24\;{\rm{cm}} = h \times \dfrac{1}{{4/3}}\\
h = 32\;{\rm{cm}}
\end{array}\]
 Therefore, the required height of object above the surface of water is 32 cm

So, the correct answer is “Option D”.


Note:
The given problem is resolved by keeping the remembrance of the concept of refractive indices along with the general mathematical relation for the apparent heights. Moreover, some basic values of refractive indices are also to be remembered.