Q16: A clear plastic cube with exactly the same index of refraction as water, is placed in a container of water. Would you be able to see the plastic cube in the water if you looked at it from an angle? Please explain why or why not.

Read this. Your answer is there.

http://www.exploratorium.edu/snacks/disappearing_glass_rods/index.html

Yes, you would be able to see the plastic cube in the water if you looked at it from an angle. The reason for this is based on the concept of refraction, which is the bending of light as it passes from one medium to another.

When light passes from air to water or from water to air, it undergoes refraction due to the change in the speed of light in different media. The amount of bending depends on the difference in refractive indices between the two media.

In this scenario, since the plastic cube has the same refractive index as water, when light passes from water into the cube or vice versa, there is no significant change in the speed of light. As a result, there is no significant bending of light at the interfaces of the cube.

Therefore, light rays entering the cube from water or exiting the cube into water will not deviate greatly from their original paths. This means that the cube will not effectively hide in the water, and it will be visible when viewed from an angle.

To determine whether the clear plastic cube would be visible in the water when viewed from an angle, we need to understand the concept of refraction. Refraction occurs when light passes through a medium and changes its direction due to the change in the medium's refractive index.

If the clear plastic cube has the same refractive index as water, it implies that light traveling through water would not experience any change in direction when it enters the plastic cube. Hence, there would be no refraction at the water-plastic interface.

Now, when we view an object through a transparent medium like water, the light rays from the object reach our eyes after passing through the water. If there is no difference in refractive index between the object and the water, the light rays will continue to travel in the same direction without any significant bending, resulting in the object being virtually invisible.

As a result, if you look at a clear plastic cube with the same refractive index as water from an angle within the water, the cube would be extremely difficult to see or may even appear invisible. This is because the light rays coming from the cube would not undergo enough refraction while passing through the water to be redirected towards your eyes.

In summary, due to the matching refractive index of the clear plastic cube and the surrounding water, the cube would be barely visible or may appear completely invisible when viewed from an angle within the water.