Final answer:
The shadow of the piece of wood will appear closer to the surface of the lake due to the refracting effect of light as it passes from air to water. The exact positioning of the shadow is influenced by various factors, hence precise calculation isn't possible without specific details.
Step-by-step explanation:
The shadow of a small piece of wood floating on the surface of a 2.5 m deep lake when the sun is just setting can be calculated using the principles of light refraction and the refractive index of water. The refractive indices of air and water cause light to refract, or bend when it moves from one medium (air) to another (water). This is often visually observed when a straight pole appears to bend when it enters water.
The refractive index for air is approximately 1.00 and for water, it is about 1.333. The angle at which the shadow forms on the bottom of the lake will not mimic the angle at which the light hits the water due to refraction. As the sun sets, the angle of incidence of the light rays is nearly parallel to the surface of water, which causes the shadow to elongate and appear closer to the surface than the actual depth of the lake. This phenomenon is referred to as the apparent depth.
That being said, the exact positioning of the shadow is influenced by other factors such as the uneven surface of the water, the size and orientation of the floating piece of wood, and the presence of any other obstructions in the water. Therefore, without specific details, we cannot calculate the exact position of the shadow.
Learn more about Light Refraction