At 08:00hrs a 2.7- m-long vertical stick in air casts a shadow 1.8 m long. If the same stick is placed at 08:00hrs in air in a flat bottomed pool of salt water half the height of the stick, how long is the shadow on the floor of the pool? (For this pool, n = 1.64.)

I can't get this for the life of me, I keep getting x= .4852 m
please tell me what i am doing wrong.

You are probably doing the refraction part right, but consider how the stick shadow is formed. It is already 1.8 m long at the surface of the water. You have to add that to the additional lateral distance that the light hitting the top of the pole refracts under water.

See how I answered the other problem that I just posted, which was of the same type.

That is a pretty high sun angle and short shadow for 8 AM, but we have to go with what they give us.

okay so i add the .4852 to the 1.8 and i get 2.2852 but it keeps saying that im wrong.

i don't understand

Isn't light bent toward the normal in the higher refractive medium?

I agree with the .4852 m lateral deflection of the beam at the top of the shadow after it enters the pool. Try answering with two or three significant figures: 2.29 m or 2.3 m. You only know the stick length to two figures, so predictions cannot be more accurate than that.

It's still wrong. I have no idea what to do at this point, but thanks for your help anyway.

I was calculating the distance of the end of the shadow from a point directly below the stick. The bottom end of the shadow is displaced the same as it is at the surface, 0.4852 m. The length of the shadow at the bottom of the pool is the same as it is at the surface: 1.8 m. This is because the rays that pass by the bottom and the top of the pool remain parallel.

I apologize for misleading you.

To solve this problem, we can use the concept of similar triangles. The ratio of the length of the stick to the length of its shadow is the same in both scenarios.

Let's define the length of the stick as "h" and the length of its shadow in the pool as "x".

In the first scenario, the stick is in the air, and the length of the stick is 2.7 m, and the length of the shadow is 1.8 m.

We can write the following proportion:

h / 1.8 = 2.7 / x

Now, we can solve for "x" by cross-multiplying:

h * x = 1.8 * 2.7

x = (1.8 * 2.7) / h

Now, in the second scenario, the stick is placed in a pool of salt water. The height of the water is half the height of the stick, so the height of the stick in the pool is h / 2.

We know that the value of "n" is given as 1.64, which is the refractive index of the salt water.

According to the laws of refraction, when light passes from air to a medium with a different refractive index, it bends. The angle of incidence (formed by the light ray and the normal line to the surface) and the angle of refraction (formed by the refracted ray and the normal line) are related by Snell's Law: n1 * sin(angle of incidence) = n2 * sin(angle of refraction).

In this case, n1 is 1 (refractive index of air), and n2 is 1.64 (refractive index of salt water).

The angle of incidence when the stick is in the air is equal to the angle of refraction when the stick is in the water. So, we can write:

sin(angle of refraction) = (1 / 1.64) * sin(angle of incidence)

sin(angle of refraction) = sin(angle of incidence) / 1.64

Since the stick is vertical, the angle of incidence is equal to the angle of refraction. So, we have:

sin(angle of refraction) = sin(angle of incidence) = sin(angle)

Using the inverse sine function, we can find the value of the angle:

angle = sin^(-1)((sin(angle)) / 1.64)

Now, we can apply the concept of similar triangles. The triangle formed by the stick, its shadow in the pool, and the line connecting the top of the stick to the end of its shadow is similar to the triangle formed by the stick, its shadow in the air, and the line connecting the top of the stick to the end of its shadow.

Since the length of the stick in the pool is h/2, and the angle is the same in both scenarios, we can use the tangent function to find the length of the shadow in the pool:

tan(angle) = (x) / (h / 2)

x = (h / 2) * tan(angle)

Now, you can substitute the value of "x" from the previous equation into this equation to find the length of the shadow in the pool.

I hope this explanation helps you understand the problem better and guides you to the correct solution.