At 08:00hrs a 2.0- 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 = 1.56.)
Use the length of the stick and the air shadow length to get the angle of incidence. It appears to me to be arctan 1.8/2.0 = 42.0 degrees Call that angle I
Next use Snell's law to get the angle of refraction (R) in the salt water.
sin I = N sin R
Solve for the angle R. N = 1.56. (That must be VERY salty water).
You can get the length of the shadow on the bottom of the pool (X) from the pool depth (D) and the refraction angle.
X/D = tan R
Answers for in sunlight, a vertical stick 9ft tall cast a shadow 7ft long.At the same time a nearby tree cast a shadow of 28ft long how long is the tree
To determine the length of the shadow on the floor of the pool, we can use the concept of similar triangles. Let's break down the problem step by step:
1. First, let's consider the situation when the stick is in the air. We have a right triangle formed by the stick, its shadow, and the vertical line from the top of the stick to the end of its shadow. The stick has a length of 2.0 meters, and its shadow is 1.8 meters long.
2. Using the concept of similar triangles, we know that the corresponding sides of similar triangles are proportional. The lengths of the stick and its shadow in the air form one pair of corresponding sides.
3. Now, let's consider the situation when the stick is placed in the saltwater pool. We have a similar right triangle formed by the stick, its shadow in the pool, and the vertical line from the top of the stick to the end of its shadow in the pool.
4. In this situation, the stick is immersed in saltwater, which has a refractive index (n) of 1.56. The refractive index is a measure of how light bends when passing through a medium. In this case, the light passes from air into the saltwater, causing the light rays to bend.
5. When the light rays bend, the angles of the triangles change, but the ratios of the sides remain the same due to the similarity of the triangles.
6. Now, let's apply the concepts of similar triangles to find the length of the shadow on the floor of the pool. Since the length of the stick is 2.0 meters and its shadow in the air is 1.8 meters, we can set up the following proportion:
(Length of stick in air) / (Length of shadow in air) = (Length of stick in water) / (Length of shadow in water)
2.0 / 1.8 = (Length of stick in water) / (Length of shadow in water)
7. Rearranging the equation, we can solve for the length of the shadow in water:
(Length of shadow in water) = [(Length of stick in water) * 1.8] / 2.0
8. To find the length of the shadow in water, we need to find the length of the stick in water. Since the stick is half-immersed in the saltwater, its height in water is half of its height in the air:
(Height of stick in water) = (Height of stick in air) / 2
(Height of stick in water) = 2.0 / 2
9. Finally, we can substitute the value we found in step 8 into the equation from step 7 to get the length of the shadow in the water:
(Length of shadow in water) = [(2.0 / 2) * 1.8] / 2.0
Therefore, the length of the shadow on the floor of the pool is 0.9 meters.