How wide is the apperature?

Question

A point source of light illuminates an aperture 2.20 m away. A 14.0 cm-wide bright patch of light appears on a screen 1.40 m behind the aperture.

How wide is the aperture?

Can someone guide me through this problem or at least put me on track. I don't expect you to just give me the answer that wouldn't be learning. Thanks.

Ahh nevermind its so easy you just use proportional triangles and the ray model of light.

Thank you for taking the time to help me understand the question and perhaps other people looking at it will have a full guide to it.

Answer 1

Use "ray tracing" and ratio and proportion. First draw a horizontal line from the point source to the screen that is 2.20 + 1.40 m long. At a distance of 2.20 m from the point source let the horizontal line be a perpendicular bisector to a line that represents the aperture (unknown height as yet). At the screen let the horizontal line be a perpendicular bisector of a line that is 14.0 cm (0.14 m) high. Now draw two lines from the point source to the ends of the line representing the spot of light on the screen. Where these two lines cross the line of unknown length, 2.20 m from the point source, is the aperture.

You now have two isosceles triangles with a common apex at the point source, the base of the smaller one being the aperture and the base of the larger being the line representing the spot of light on the screen. Since these are similar triangles, you know the ratio of their heights is the same as the ratio of their bases. Plug in the numbers and solve for the aperture width.

Answer 2

First, draw it out with everything you know and you will see that you have two identically shaped triangles: one big one with a base of 0.14m and a height of 2.2+1.4m. And one smaller one inside that one with a height of 2.2m and an unknown base (your aperature size that you need to find.)

Since the triangle have identical angles, the sides will be proportional. Just set up your proportions that you know (big base/big height = small base/small height) and solve that equation for your unknown and there you have it!