Question

Suppose that you spotted a fish swimming in a peaceful lake. It seemed to you that the fish was 1 meter underneath the water surface. Assume that you directed your sight along a line that was perpendicular to the water surface when you saw the fish. What was the actual distance from the fish to the surface?

Answer 1

When an object is viewed from above the water surface, it appears to be shallower than it actually is due to refraction. In this case, the actual distance from the fish to the surface would be 0.751 meters.

Step-by-step explanation:

When an object is viewed from above the water surface, it appears to be shallower than it actually is due to a phenomenon called refraction. Refraction occurs when light waves pass from one medium (air) into another medium (water) and change speed and direction. In this case, as light waves from the fish enter the water, they slow down and bend towards the normal, causing the fish to appear closer to the surface than it really is. The actual distance from the fish to the surface can be calculated using the formula:

Actual distance = Apparent distance / Refractive index

where the refractive index is the ratio of the speed of light in air to the speed of light in water. In this case, the apparent distance is 1 meter and the refractive index is approximately 1.33. Plugging in these values, the actual distance from the fish to the surface is:

Actual distance = 1 meter / 1.33 = 0.751 meters

Answer 2

To develop this problem we will apply the concepts related to the apparent depth.

The apparent depth is a relationship between the measured distance and the refractive coefficient of the medium in which the measurement is made.

Theoretically, this coefficient for water is n = 1.33 and the formula can mathematically be described as

`d_(app) = (d)/(n_w)`

Now what you need to find is the real distance, rearranging the equation

`d = d_(app)n_(w)`

Replacing,

`d = 1*1.33`

`d = 1.33 m`

Therefore the actual distance from the fish to the surface is 1.33m