a circular opaque disk, 25 cm in diameter, is set up 30 cm from a circular source of light of diameter 40 cm. Ascreen is placed 30 cm beyond the opaque disk. Describe, giving dimensions, the nature of the shadow on the screen.
Ok, I have drawn a sketch and can say that the shadow formed is the umbra which is in the middle surrounded by 2 other sections called penumbra.
how do i calculate the shadow?
Well, calculating the shadow can be a bit of a drag, but no worries, I'm here to help!
To figure out the dimensions of the shadow, we need to consider a few things. First, let's find the diameter of the umbra. We know that the diameter of the opaque disk is 25 cm and the distance between the disk and the light source is 30 cm.
Using some fancy math, we can calculate that the diameter of the umbra (the darkest part of the shadow) is equal to (diameter of the opaque disk x distance between the disk and the light source) divided by (distance between the disk and the screen).
So, let's crunch the numbers:
Umbra diameter = (25 cm x 30 cm) / 30 cm
= 25 cm
The umbra diameter turns out to be the same as the diameter of the opaque disk!
Now, the penumbra is the lighter part surrounding the umbra. Its dimensions depend on the diameter of the light source and the distance between the disk and the light source.
Since the diameter of the light source is 40 cm and the distance between the disk and the light source is also 30 cm, we can calculate the diameter of the penumbra by using the same formula.
Penumbra diameter = (diameter of the light source x distance between the disk and the light source) / (distance between the disk and the screen)
Penumbra diameter = (40 cm x 30 cm) / 30 cm
= 40 cm
So, the diameter of the penumbra is 40 cm.
To sum it up, the nature of the shadow on the screen is an umbra with a diameter of 25 cm in the middle, surrounded by a penumbra with a diameter of 40 cm.
I hope that sheds some light on the situation for you!
To calculate the dimensions of the shadow, we need to consider the relative positions and sizes of the objects involved. In this case, we have a circular opaque disk with a diameter of 25 cm, and a circular source of light with a diameter of 40 cm.
Since the opaque disk is smaller than the source of light, there will be a shadow formed on the screen. The nature of the shadow consists of three parts: the umbra, which is the darkest area in the center, and the penumbra, which is the partial shadow surrounding the umbra on both sides.
To determine the dimensions of the shadow, we can use similar triangles.
Let's consider the following distances:
- Distance from the light source to the opaque disk (L1) = 30 cm
- Distance from the opaque disk to the screen (L2) = 30 cm
Now, we can set up a proportion using the similar triangles formed by the light source, the opaque disk, and the shadow on the screen:
(L2)/(L1) = (Shadow Diameter)/(Opaque Disk Diameter)
Substituting the known values:
30 cm / 30 cm = Shadow Diameter / 25 cm
Simplifying the equation:
1 = Shadow Diameter / 25 cm
To find the diameter of the shadow, we can multiply both sides of the equation by 25 cm:
Shadow Diameter = 25 cm
Therefore, the diameter of the shadow on the screen will be 25 cm.