Calculation light reflection area

[Alferd]

There are a place installed eclipse shape of mirror to reflect the sunlight to the area that is not enough sunlight in the town. In this case, they installed 51 square meter mirror and provide the sunlight to the area of 600 square meter with the mirror located 450 meter above the town. Can I know what is the formula to calculate the area of sunlight reflection?

https://www.visitnorway.com/listings/the-giant-sun-mirrors-in-rjukan/3632/

[exchemist]

42 minutes ago, Alferd said:

There are a place installed eclipse shape of mirror to reflect the sunlight to the area that is not enough sunlight in the town. In this case, they installed 51 square meter mirror and provide the sunlight to the area of 600 square meter with the mirror located 450 meter above the town. Can I know what is the formula to calculate the area of sunlight reflection?

https://www.visitnorway.com/listings/the-giant-sun-mirrors-in-rjukan/3632/

I'm not quite sure what you want to know. Do you mean a formula for the rate of divergence of the beam? That's obvious, surely, if it grows from 51m² to 600m² , i.e. a factor of 11.6, over the course of 450m? Or do you want to know why it diverges at that rate? That would be more complicated - some function of the shape of the mirrors, I imagine.   

[Genady]

1 hour ago, Alferd said:

There are a place installed eclipse shape of mirror to reflect the sunlight to the area that is not enough sunlight in the town. In this case, they installed 51 square meter mirror and provide the sunlight to the area of 600 square meter with the mirror located 450 meter above the town. Can I know what is the formula to calculate the area of sunlight reflection?

https://www.visitnorway.com/listings/the-giant-sun-mirrors-in-rjukan/3632/

What is "eclipse shape of mirror"? In the article, the mirrors appear to be flat.

[Alferd]

Thank you for your quick reply. I want to know the formula of the rate of divergence of the beam.

[Genady]

Some clarifications here: optics - Is light dispersed over distance by flat mirrors? - Physics Stack Exchange

[swansont]

Light doesn’t need to diverge for this implementation. A 1 m^2 non-diverging beam projected on to the ground will cover more than that area if the angle isn’t 90 degrees. Probably by 1/sin(theta)

[exchemist]

4 hours ago, Alferd said:

Thank you for your quick reply. I want to know the formula of the rate of divergence of the beam.

@swansont is quite right of course: I wasn’t thinking. We need more information. What is the shape of the mirrors, what is the shape and dimensions of the 600sq m illuminated area and what is the angle of the beam to the ground? Is a diagram available?

[Genady]

Perhaps, the pictures here, Giant Sun Mirrors of Rjukan – Rjukan, Norway - Atlas Obscura, give the idea. The mirrors are flat, and the light spot is not big.

More story and pictures here: The dark town that built a giant mirror to deflect the Sun - BBC Future.

[Alferd]

I think this mirror should be convex mirror with the total area 51 square meters of three giant mirror

[Genady]

1 hour ago, Alferd said:

I think this mirror should be convex mirror with the total area 51 square meters of three giant mirror

If the mirrors were convex it would show in this picture: