Question

A cicular opaque disk, 25cm in diameter, is set up 30 cm from a circular source of light of diameter 40 cm. A screen is placed 30cm beyond the opaque disk. Describe, giving dimensions, the nature of the shadow on the screen.

Answer 1

In all the time you've spent posting this problem, have you tried studying your text, or heck, just thinking about it?

Draw a diagram of the scene seen edge-on.

Let the line MN representing the edge of the mirror extend from M=(0,20) to N=(0,-20)

Let the line AB representing the disc extend from A=(30,12.5) to B=(30,-12.5)

Let the screen be drawn at x=60

Extend line MA to V on the screen
Extend line MB to W
Extend line NA to X
Extend line NB to Y

The line VX represents the diameter of the umbra, since it is in the shadow of all light points between M and N

Lines VY and XW represent the ring of the penumbra, since they are illuminated by some rays from the light.

A little algebra reveals that

XV = 15.625
VY = 45 - 15.625 = 29.375

So, the umbra is a disc of diameter 31.25cm

the penumbra is a ring around the umbra, with diameter 90cm

Answer 2

what is the algebra to reveal
xv=15.625?
trying to get my head around this but it is not sinking in

Answer 3

Actually, I messed up.
M=(0,20) A = (30,12.5)
The line MA has slope -1/4 (-7.5/30)
So, XV = 5

The line NA has slope 32.5/30 = 65/60
So, Y is (60,45), and VY = 40

this changes the diameter of the umbra, but not the penumbra.

Answer 4

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