Question

A fish appears to be 2.00 m below the surface of a pond (nwater = 1.33) when viewed almost directly above by a fisherman. What is the actual depth of the fish?

Answer 1

Step-by-step explanation:

The given data is as follows.

Apparent depth = 2.00 m, refractive index = 1.33

It is known that formula to calculate real depth is as follows.

The refractive index =
`\frac{\text{real depth}}{\text{apparent depth}}`

or, real depth = refractive index × apparent depth

Now, putting the given values into the above formula as follows.

real depth = 1.33 × 2

= 2.66 m

Thus, we can conclude that the actual (real) depth of the fish is 2.66 m.

Answer 2

Actual depth = 2.66 m

Step-by-step explanation:

Given:

Apparent depth = Depth of fish as seen below the surface of water =
`D_(a)` = 2 m

Refractive index of water = n = 1.33

Actual depth is related to the apparent depth as follows:

n =
`D_(r)` /
`D_(a)`

⇒ Actual depth =
`D_(r)` = n ×
`D_(a)`

= (1.33) ( 2 ) = 2.66 m