How Does a Sharp Shadow Prove Light Travels in Straight Lines?

[logearav]

Homework Statement

If an opaque object is placed between a source of light and a screen, a sharp shadow is obtained on the screen. This shows that light travels in straight lines. I don't understand this statement...How a sharp shadow on the screen proves that light travels in straight line?

Homework Equations

The Attempt at a Solution

 

[Fewmet]

Consider these two images:
http://www.win.tue.nl/~wstahw/2IV05/Point_light_source_sharp_shadow.png
http://www.win.tue.nl/~wstahw/2IV05/Area_light_source_soft_shadow.png

The shadows edge in the former is quite distinct. If you were to draw lines from a point source of light, tangent to the edge of the sphere and onto the table top, they would form such a show. There would be a clear demarcation between where it is light and where it is dark.

If that line of light, however, were to bend a variable amount around the edge of the sphere, the border between light and dark would be more like what is shown in the latter image. It would grade from all dark to less dark to all light.

That soft edge happens in the second image because the light source is not a point or even a good approximation of a point. That gives an effect like the http://www.sems.und.edu/FrameA/LunarEclipses/lunar4.jpg" in an eclipse. Note in the eclipse image that the straight lines of light give partial shadow in the penumbral region.

 

[logearav]

Sir, i don't understand clearly. Can u give some other example, please?

 

[cupid.callin]

let the light be coming from left andf making an image ap point P (there is a screen at P)
if now ou place a small object before P you will see a shadow (enlarged, depending on the distance b/w P and object)

now you can argue that light can turn a little and cross is object from side and then again meet at P ... making an image again ... which doesn't happen

so light cannot change its way on its own (coz its not forming an image)
therefore light must travel in straight line

 

[Fewmet]

Sir, i don't understand clearly. Can u give some other example, please?

I have been thinking more about this. Maybe I am reading too much into your question, but I am not crazy about my answer either. First let me try to be clearer about what is meant by saying light traveling in a straight line creates a sharp shadow.

I am assuming you get that "sharp" shadow has very clear edge: you can say clearly "Here is the line where it stops being dark and starts being light". There is no gray between lit and unlit.

How would straight beams of light cause that? I think http://en.wikisource.org/wiki/File:PSM_V04_D690_Formation_of_a_shadow.jpg" shows that well: those are straight lines of light that graze the edge of the sphere. The shadow is created where the light rays are prevented from falling. If light moved in a path that curved around the edges of the sphere, some light would fall in the area shown shadowed in that image.

Here is the problem with the answer: suppose the light did curve around the sphere. If all the light bent, it looks like there could still be a sharp (albeit smaller) shadow. So is this really evidence that light moves in a straight line?

Having thought through that by writing it, something else occurs to me. If the beams tangent to the sphere bent one degree and the "adjacent" beams went straight, there would be a gray ring around the shadow and the shadow would n longer be sharp. And if those beams bent, you could make the same argument about the next ones over...

 

[logearav]

Now, I got it Mr. Fewmet. Thanks a lot.
Thanks to mr.cupid.calin for replying this thread.

 

[Fewmet]

Now, I got it Mr. Fewmet. Thanks a lot.
Thanks to mr.cupid.calin for replying this thread.

I am happy to help and glad that you asked. I've often seen the claim that sharp shadows mean light travels in a straight line, and did not question it as carefully as I should have. Your asking for clarification made me think more deeply and see the compelling truth of the statement.

 

[cupid.callin]

but funny thing is that the statement "Light travels in straight line" is not completely true.

It will bend if it encounter an obstacle of size comparable to light's wavelength viz very small so we don't observe bending in daily life

 

[Fewmet]

but funny thing is that the statement "Light travels in straight line" is not completely true.

It will bend if it encounter an obstacle of size comparable to light's wavelength viz very small so we don't observe bending in daily life

Yeah, I was danging around that...