Can someone help please?
A circular opaque disk, 25 cm in diameter, is set up 30 cm from a circular source of light of diameter 40 cm. A screen is placed 30 cm beyond the opaque disk. Describe, giving dimensions, the nature of the shadow on the screen
To describe the nature of the shadow on the screen, we need to consider the position and size of the objects involved - the light source, the opaque disk, and the screen.
First, let's define the objects' positions and dimensions:
1. Light source: The circular source of light has a diameter of 40 cm.
2. Opaque disk: The circular opaque disk is positioned 30 cm in front of the light source. It has a diameter of 25 cm.
3. Screen: The screen is placed 30 cm beyond the opaque disk, meaning it is 60 cm away from the light source. The screen's dimensions are not given.
Now, let's analyze the situation:
When the light passes through the opaque disk, it will create a shadow on the screen. The shadow will have two parts:
1. Umbra: The umbra is the dark central part of the shadow that is directly behind the opaque disk. Its width can be calculated by subtracting the diameter of the opaque disk from the diameter of the light source: (40 cm - 25 cm) = 15 cm. Therefore, the umbra on the screen will have a width of 15 cm.
2. Penumbra: The penumbra is the lighter, surrounding area of the shadow. It is caused by the partial obstruction of light by the opaque disk. To calculate the width of the penumbra, we need to consider the distance between the light source and the screen. Since the screen is 60 cm away from the light source, we need to find the ratio of the diameters of the light source and the total distance:
Penumbra width = (diameter of light source / total distance) * distance from the opaque disk to the screen
Penumbra width = (40 cm / 60 cm) * 30 cm
Penumbra width ≈ 20 cm
Therefore, the penumbra will have a width of approximately 20 cm on the screen.
In summary, the nature of the shadow on the screen will consist of a central dark area called the umbra, with a width of 15 cm, surrounded by a lighter area called the penumbra, with a width of approximately 20 cm.