a fish that you are looking at from a boat seems to be 20cm below the water surface. the actual depth of the fish is

realdepth/apparentdepth = refractive index of water.

Since water's r.i. = 4/3,
the actual depth is 4/3 * 20 = 80/3 = 26.7 cm

To determine the actual depth of the fish, we can use a concept called refraction. Refraction occurs when light passes through different mediums, such as air to water, and causes the light rays to change direction.

To measure the actual depth of the fish, we need to consider the refraction of light at the air-water interface. For this calculation, we can use Snell's Law, which states:

n1 * sin(angle of incidence) = n2 * sin(angle of refraction)

In this case, n1 represents the refractive index of air (approximately 1), and n2 is the refractive index of water (approximately 1.33). The angle of incidence is the angle at which light enters the water, and the angle of refraction is the angle at which it bends after entering the water.

Let's assume that the angle of incidence (the angle between your line of sight and the water surface) is θ. We can use trigonometry to find the angle of refraction. Since the fish appears 20 cm below the water surface, it forms the base of a right-angled triangle with the hypotenuse being the line connecting your eye to the fish.

Using basic trigonometry, we can infer that the opposite side of the triangle is 20 cm and the adjacent side represents the distance from the fish to your eye (let's call it d).

Now, we can use the sine function to find the angle of refraction:

sin(θ) = opposite / hypotenuse
sin(θ) = 20 cm / d

Next, we can use Snell's Law to get the actual depth of the fish:

n1 * sin(θ) = n2 * sin(θ')
1 * (20 cm / d) = 1.33 * sin(θ')

Simplifying the equation, we have:

20 / d = 1.33 * sin(θ')

Next, we need to find the value of sin(θ'). We can rearrange the equation and isolate sin(θ'):

sin(θ') = (20 / d) / 1.33

Finally, we can calculate the actual depth of the fish (d') using the equation:

d' = d * sin(θ')

By substituting the value of sin(θ') from the previous calculation, we get:

d' = d * [(20 / d) / 1.33]

Simplifying further, we have:

d' = 20 / 1.33

Therefore, the actual depth of the fish is approximately 15.04 cm.