Question

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?

Answer 1

x = 0.04 m , length of the second sheet cut

Step-by-step explanation:

Given:

- The distance from the source to second scare cut x = 0.25

- The distance from the source to first scare cut x = 0.5

- The length of the first square cut L_2 = 0.08

- The length of the second square cut is x

Find:

What is the length of the side of the hole in this first sheet?

Solution:

- A small sketch of the scenario in 1-D view from top would help us in determining the the length of the first square cur sheet. (See Attachment)

- In lieu, to the diagram attached. We will use the concept of similar triangles. We see that the two triangles ABC and ADE are similar.

- Where BC and DE denote half of their original lengths, as follows:

BC = 0.5*x

DE = 0.04 m

AB = 0.25 m

AD = 0.5 m

- Using similar triangles we have:

AB / AD = BC / DE

- Plug in the variables:

0.25 / 0.5 = 0.5*x / 0.04

x = 0.04 m