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A point source is fixed 1.0 m away from a large screen. Call the line normal to the screen surface and passing through the center of the point source the zaxis. When a sheet of cardboard in which a square hole 0.080 m on a side has been cut is placed between the point source and the screen, 0.50 mfrom the point source with the hole centered on the zaxis, a bright square shows up on the screen. If, instead, a second sheet of cardboard with a similar square hole is placed between the point source and screen, 0.25 m from the point source with the hole centered on the z axis, the bright square it casts on the screen is identical to the bright square from the first sheet.What is the length of the side of the hole in this sheet?

Respuesta :

cjmejiab

Answer:

d=0.02m

Explanation:

The key of the exercise is to be able to graph the problem to be able to develop it. After that you simply proceed through a triangular relationship.

Then I leave the graph of the problem and give the solution.

So things, under the given relationship, we have,

[tex]\frac {0.04} {0.5} = \frac {d} {0.25}[/tex]

*The value of 0.04 is taken because the triangle given in the graph must be divided in half, to obtain rectangular triangles.

[tex]d = \frac {0.04 * 0.25} {0.5}[/tex]

[tex]d = 0.02m[/tex]

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okpalawalter8

We have that from the Question  it can be said that  the length of the side of the hole in this sheet is

[tex]d_1=0.04m[/tex]

From the Question we are told

A point source is fixed 1.0 m away from a large screen. Call the line normal to the screen surface and passing through the center of the point source the z-axis. When a sheet of cardboard in which a square hole 0.080 m on a side has been cut is placed between the point source and the screen, 0.50 m from the point source with the hole centered on the z-axis, a bright square shows up on the screen. If, instead, a second sheet of cardboard with a similar square hole is placed between the point source and screen, 0.25 m from the point source with the hole centered on the z axis, the bright square it casts on the screen is identical to the bright square from the first sheet.What is the length of the side of the hole in this sheet?

Generally the equation for the new distance is mathematically given as

[tex]\frac{d_2}{0.5}=\frac{d}{0.25}\\\\Therefore\\\\d_1=\frac{0.08*0.25}{0.5}\\\\[/tex]

[tex]d_1=0.04m[/tex]

Therefore

the length of the side of the hole in this sheet is

[tex]d_1=0.04m[/tex]

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