A large bowl contains water 10cm deep and has a small electric lamp at the bottom.A disc of cardboard is floating on the surface with its centre vertically above the lamp,and is of such diameter that the lamp can just not be seen by a person looking into the water.calculate the diameter of the disc.
22,6cm
22,6 cm
22.6 cm
To calculate the diameter of the disc floating on the surface, we need to consider the physics of refraction and the behavior of light when it passes from one medium (air) to another (water).
Here are the steps to solve the problem:
1. Determine the critical angle: The critical angle is the angle at which the light rays passing from water into air will be completely internally reflected back into the water. The critical angle can be calculated using the equation:
critical angle = arcsin(n2/n1)
In this case, n1 is the refractive index of water (approximately 1.33), and n2 is the refractive index of air (approximately 1.00). Plugging in these values, we get:
critical angle = arcsin(1.00/1.33)
2. Measure the apparent depth: The apparent depth is the depth at which an object appears to be submerged when viewed from a different medium. In this case, the lamp is at the bottom of the bowl, and its light passes through the water to reach the observer's eye. The apparent depth can be calculated using the equation:
apparent depth = real depth / refractive index
In this case, the real depth is 10 cm, and the refractive index is 1.33. Plugging in these values, we get:
apparent depth = 10 cm / 1.33
3. Calculate the height of the disc: Since the disc is floating on the surface and its center is vertically above the lamp, the light from the lamp will pass through the water and cardboard, and then into the air. The light rays from the top and bottom of the lamp will follow different paths due to refraction.
The height of the disc can be calculated by subtracting the apparent depth from the real depth. In this case:
height of disc = real depth - apparent depth
4. Calculate the diameter of the disc: The diameter of the disc will be twice its radius. We can use the height of the disc to calculate the radius by assuming that it is a uniform circular disc.
diameter of disc = radius of disc * 2
To find the radius, divide the height of the disc by 2:
radius of disc = height of disc / 2
5. Plug in the calculated values to get the diameter of the disc.
diameter of disc = (height of disc / 2) * 2
Make sure to convert the measurements to the same unit if necessary.
Following these steps should allow you to calculate the diameter of the disc floating on the water.