Why Does a Nearby Light Source Produce a Blurry Shadow?

[Pranav Jha]

I was wondering why does a large, nearby light source produces a somewhat blurry shadow?

While looking for a reply i found that when we are close to own own shadow, the outline of your shadow is sharp because the Sun is so far away. But i couldn't quite understand it.

 

[Mu naught]

mainly because there is a lot of reflected light from nearby objects, which partially illuminates the dark region.

if however you were to remove all reflecting surfaces you still would not get a perfectly crisp edge due to diffraction, which is simply a consequence of the wave-like nature of light.

 

[Pranav Jha]

mainly because there is a lot of reflected light from nearby objects, which partially illuminates the dark region.

In that case if the distance increased, the number of objects reflecting the light would increase as well. So, if the distance were larger, the larger source should produce an even more blurred shadow shouldn't it?

 

[DaveC426913]

No. No no no. It has absolutely nothing to do with diffusion of light or secondary reflections.

A LARGE nearby light source will cast a blurry-edged shadow. There is a wide zone on the ground where the object casting the shadow only managed to eclipse PART of the LARGE light source. This forms the body of the soft edge of the shadow.

It's exactly like the umbra and penumbra of the Moon's shadow during an eclipse.


Likewise, if the object is CLOSE to its background, then the non parallel rays (from the left and right edges of the sun's disc) diverge very little, so the shadow is sharp-edged. If the object is FAR from its background, the rays are able to diverge more, forming a softer edged shadow.


If you position yourself where the shadow would strike, and look back toward the object and light source behind it, you will see that you will have to move a goodly distance from side-to-side to move from fully lit to fully blocked. Everything in between those two will have you seeing the large light source only partially hidden behind the object - which means this spot is only partially lit.

 

[Pranav Jha]

No. No no no. It has absolutely nothing to do with diffusion of light or secondary reflections.

A LARGE nearby light source will cast a blurry-edged shadow. There is a wide zone on the ground where the object casting the shadow only managed to eclipse PART of the LARGE light source. This forms the body of the soft edge of the shadow.

.


could you please explain this further

 

[DaveC426913]

To sum: Place a large light source (such as a light with a reflecting parabola) shining on an object. The object will cast a soft-edged shadow. You can change the softness of the shadow's edge by changing th size of the light, by moving the light closer or farther from the object, or by moving the obejct closer or farther from the background.

Why?

Place yourself where the object's shadow is cast, looking back toward the object. What will you see? There are three possibilities

1] If you place yourself anywhere in the shadow of the object, looking back towadf the object, you will only see the object. You will not be able to see the light, which is directly behind the object, right?

2] If you place yourself well outside the shadow of the object, you will see the object to one side, and you will see the light, shining unobstructed, in its full glory, next to it.

3] What if you place yourself right on the border between light and shadow? What do you see now? You see the object, and behind the object - partially obscured by the object - the light source. How much of the light source is obscured? Depends on where you position yourself. You can move back and forth between shadow and fully lit as you wish but, because the light source is large, you may have to move back and forth by a several inches or a foot. Now turn around and look at the background - there is a band a foot wide in which the background is only partially unlit.

 

[Pranav Jha]

okay. But shouldn't the rays of light spread even further at greater distances and thus produce more blurred shadows?
Also, why is it just the opposite in the case of small light sources that is they produce clear shadows at smaller distances but blurred shadows at larger distances?

 

[Pranav Jha]

i can understand the relation between the object and background but am confused about the relation between the distance of the object and source of light casting the shadow

 

[DaveC426913]

okay. But shouldn't the rays of light spread even further at greater distances and thus produce more blurred shadows?

Yes, of course.

Also, why is it just the opposite in the case of small light sources that is they produce clear shadows at smaller distances but blurred shadows at larger distances?

That is not "opposite" at all. That's exactly the same.

All shadows will be sharper if the object is closer to the background.

 

[DaveC426913]

i can understand the relation between the object and background but am confused about the relation between the distance of the object and source of light casting the shadow

Draw a picture.

Draw the light source (large/small), the object and the background. Play with the distances.

Draw lines showing how rays of light from both edges of the light source will encompass the object, but by the time they reach the background will be farther apart. Size of light soruce, distance of light source from object and distance of object from background will all have an effect on sharpness of shadow edge.

 

[K^2]

I think he expects light from Sun to diffuse because it's so far away.

But light travels in a straight line through vacuum. So if we neglect atmospheric effects (which do soften shadows as well, but that's a different topic) the only factor is how big the Sun appears. In other words, what fraction of the sky does the Sun take up. The Sun is big, but it's also very far away. It's size is about 1/100th of its distance to Earth, so the soft part of the shadow (penumbra) will have depth of 1/100th of the distance the object is from the background. E.g. a ball 1m above ground will cast a shadow with 1cm penumbra if Sun is directly above.

 

[Pranav Jha]

A LARGE NEAR source castes blurred shadow and LARGE FAR AWAY source also castes a blurred shadow, then where are we supposed to place the light source to get an acute shadow?

 

[Pranav Jha]

I think he expects light from Sun to diffuse because it's so far away.

It's size is about 1/100th of its distance to Earth, so the soft part of the shadow (penumbra) will have depth of 1/100th of the distance the object is from the background. E.g. a ball 1m above ground will cast a shadow with 1cm penumbra if Sun is directly above.

can you help with how that is derived mathematically?

 

[Pranav Jha]

Yes, of course.


That is not "opposite" at all. That's exactly the same.

All shadows will be sharper if the object is closer to the background.

I was not referrring to the distance between the object and the background but to the distance between the object and the small light source.

My book states that A large, nearby light source produces a somewhat blurry shadow

 

[DaveC426913]

I was not referrring to the distance between the object and the background but to the distance between the object and the small light source.

My book states that A large, nearby light source produces a somewhat blurry shadow

Yes. It will. Why are you having a problem with this?

Any non-point light source will form a http://en.wikipedia.org/wiki/Umbra" (i.e. partial) shadow. The larger the light source, the larger the penumbra.

 

[DaveC426913]

can you help with how that is derived mathematically?

He just did.

Seriously, draw some sketches.

 

[Pranav Jha]

yeah, the sketches helped greatly
the size of umbra for the smaller light source is increasing with distance whereas it is getting smaller for the larger light source.
So, for a given distance, a smaller light source always produces a sharper shadow than the larger right source, am i correct?
Also, i was wondering if the sharpness of the shadow depends on the size of umbra alone, size of penumbra alone or the ratio of the sizes of umbra and penumbra?

 

[Pranav Jha]

the reason why i asked the question was in the case of the smaller light source, the umbra as well as the penumbra is increasing in size. So, i don't know if the shadow will be more sharp or less sharp

 

[Pranav Jha]

but in the case of large source the penumbra is increasing in size while umbra is decreasing in size, so i can be sure about the sharpness of the shadow decreasing