Maximum light through the window

In summary, the total perimeter of the window is 10m and we need to find the dimensions that will allow for maximum light to come through the window. The property that determines the amount of light is the area of the window, which is the sum of a rectangle and a semi-circle. By letting $x$ be the width and $y$ be the height, we can find the radius of the semi-circle and use it to find the maximum area.
  • #1
marutkpadhy
9
0
A window is in the form of rectangle surmounted by a semi circle. The total perimeter of the window is 10m. Find the dimensions of the window to admit maximum light through the whole opening.
 
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  • #2
What property of the window is it that determines the amount of light that comes through?
 
  • #3
Area
 
  • #4
marutkpadhy said:
Area

Correct! :D

So, we need to find the area of the window, which is the sum of a rectangle and a semi-circle, and somehow get the given perimeter involved. Suppose we let $x$ be the width of the rectangle and $y$ be the height. If the semi-circle sits on top of the rectangle, what then is its radius?
 

Related to Maximum light through the window

What is the best direction for maximum light through a window?

The best direction for maximum light through a window depends on the location and orientation of the window. In general, south-facing windows receive the most sunlight throughout the day. However, east-facing windows are ideal for morning light and west-facing windows are best for afternoon light.

How can I increase the amount of light coming through my window?

There are a few ways to increase the amount of light coming through your window. One option is to keep the window clean and free from any obstructions or debris. You can also consider installing reflective window film or using lighter-colored curtains or blinds to reflect more light into the room.

Does the size of a window affect the amount of light it lets in?

Yes, the size of a window does affect the amount of light it lets in. Larger windows allow more light to enter a room compared to smaller windows. Additionally, windows that are taller and narrower tend to let in more light than shorter and wider windows.

Can the angle of a window affect the amount of light it lets in?

Yes, the angle of a window can affect the amount of light it lets in. Windows that are more perpendicular to the sun's rays will let in more light compared to windows that are at a more acute angle. This is why south-facing windows receive the most sunlight throughout the day.

What factors can impact the amount of light coming through a window?

Aside from the direction, size, and angle of a window, there are other factors that can impact the amount of light coming through a window. These include the weather (cloudy or sunny), the time of day, the season, and any obstructions outside of the window such as trees or buildings.

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