# Length of a shadow

1. Apr 6, 2015

### Helpless guy

1. The problem statement, all variables and given/known data

Hi everybody; a teacher of mine has given me a photo of two street lampd and their shadows; he has said to me that it's height is 3 metters, and the distance between the lamps is metters, and with that information I should be able to tell the lenght of the shadow.

The image is taken from the top of a building, so I see the shadow making an angle with the lamp.
2. Relevant equations
I have measured the distances of both, the shadow and the distance between lamps, which are 6.7 and 4.7 cm.
3. The attempt at a solution
If I use a rule of three I can find the value of the lenght of the shadow, but the fact that the photo is taken from a certain height makes me uncomfortable, because I don't know if I am measuring the actual lenght or just a projection.

Thanks for Reading.

2. Apr 6, 2015

### Avatrin

Let see... If I have understood this correctly, you have an image of two street lamps and their shadows. You know the height of the lamps, and the distance between the lamps. The task is to find the length of the shadows they cast, and I assume the source of light is the sun. However, measuring the length of the shadow using a ruler and using proportions is not possible because the photo is taken from a weird angle.

Do you know the angle of the sunlight relative to the street lamps? That way it will boil down to a simple trigonometric problem. I assume the street is horizontal enough for the shadows to be at a right angle to the street lamps. That way, the two street lamps with their shadows form two right angled triangles.

I think you have to make some assumptions to solve this problem. Usually, if you state what assumptions you have made, and if these assumptions make sense, the answer you give will be seen as being correct. Often, the ability to make appropriate kinds of assumptions is what is really being tested in homeworks.

3. Apr 7, 2015

### physicsquestion

maybe upload the image?

4. Apr 8, 2015

### haruspex

Is Avatrin's interpretation correct? If so, one assumption likely to be be needed is what point in the photograph represents the photographic target, i.e., the logical centre of the picture. Even then, I doubt there's enough information.
You only mention one pair of measured lengths (in the photo) for the height of post and length of shadow, but the two will be different, no? And have a different ratio?
It seems to me that the question is equivalent to having a photograph of a rectangular 3D framework (edges of a box) and being asked to deduce one dimension given the other two. I believe I can prove that that cannot be solved in general.

5. Apr 8, 2015

### Helpless guy

You are right, the photo is taken from the top of a building, the shadow makes a small angle of 4 degrees with the lamp itself, I have checked that the lamp is almost paralel to to the edge of the photo., so the only I can think of is saying that since the angles are small, if I am measuring any kind of projection, it will be very close to the actual distance.

I rather not, I don't know if my teacher would like it if he ever foud out that I have uploaded that photo to the internet. But I have made a schematic representaion http://postimg.org/image/kw8gg9eg5/

6. Apr 8, 2015

### Avatrin

Yes, I am quite certain you are not expected to give an exact answer. So, as long as you write down this assumption alongside your answer, it should suffice.

7. Apr 8, 2015

### Helpless guy

Thank you very much for your anwsers, I am almost sure I have to say that is only thanks to the small angle that I can measure the distance on the photo because of the small angle; I have made some experiments with the shadows of two books and a table lamp, only for small angles the distances measured on the photos were similar to the actual lenght of the shadow.

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