How will light react in this situation....

[xrayspecs]

Dear Physics Forum,

I need help with this problem. In the diagrams above I try to show my difficulty. My main problem is working out how shadow will fall on a completely flat surface with the light source at more or less a 0 or 180 degree angle (depending on how you want to look at it) . Through internet searches I have seen how it is possible to calculate the shadow in a natural setting at around 45 degrees.

From knowledge acquired at school and light research... (pun intended) I know light travels in straight lines. So if it met a completely flat surface how would it be possible to work out where the shadow of the shape would appear on the ground? And how long it would measure on said ground?

Please let me know if you need any more information or drawings to try and make this situation easier to understand.
Any help will be most appreciated!

Thank you for reading,

Xrayspecs

 

[A.T.]

And how long it would measure on said ground?

Infinite, if the ground is an infinite flat plane.

 

[DrStupid]

I know light travels in straight lines.

Yes, but the problem is that different straight lines don't necessarily have the same direction.

So if it met a completely flat surface how would it be possible to work out where the shadow of the shape would appear on the ground?

In general you need to find the intersection of the shadow volume with the ground. In case of a sphere and a point source the shadow volume is a cone and the intersection with the ground is an ellipse, parabola or hyperbola. In case of real bodies and light sources it will me much more complex. This kind of calculations is what GPUs are build for.

And how long it would measure on said ground?

As mentioned above this can be quite difficult to answer, especially if the shape of the object is not clearly defined. But you can at least estimate the maximum length of the umbra. It is the distance where the object has the same angular diameter as the light source. In sunlight that would be 106 to 109 times the size of the object.

 

[kuruman]

You have to understand that the picture you drew is misleading. The Sun is so far away that its rays are parallel at any given location. A modified picture is shown below. What do you think the shadow would be like on the flat plane? Remember that shadow is the absence of light. In the picture below, what light, which would normally fall on the plane, is blocked by the object?

 

[Redbelly98]

If we're treating the sun as a point source (which it isn't), then the shadow would lie between the two thin lines in the OP -- the ones that eminate from the lower-left and lower-right "corners" of the object. And as A.T. said, it would extend to infinity.

If we're treating the sun as an extended source, then each of those lines becomes a pair of lines, at roughly 0.5 degrees to each other. In between the two lines, there is a transition from fully bright to fully dark. But the shadow still extends to infinity.

The answer to the question "How would I show this curve?", is that you would not show it at all.

 

[Lnewqban]

... how shadow will fall on a completely flat surface with the light source at more or less a 0 or 180 degree angle...

The problem I see is the difficulty to achieve that angle in nature.
Even before the Sun rises, some light hits our eyes and objects.
That light comes from reflection on dust particles, bottom of clouds, etc.

If the object is tall enough, the shadow could be seen on the clouds.

 

[jbriggs444]

If we are treating the sun as a point source then there is no shadow in the first place. The surface is not illuminated.

 

[xrayspecs]

Thank you for your comments!