A point source of light illuminates an aperture 4.00m away. A 18.0 cm -wide bright patch of light appears on a screen 2.00m behind the aperture.

I have been trying to use the equation w=(2*wavelength*distance)/aperature width. However, I am not given wavelength and the type of light is not specified. Also, does the source of light being 4.00m away from the aperature even matter?

The equation you mentioned, w = (2 * wavelength * distance) / aperture width, is known as the diffraction formula. It relates the width of a diffraction pattern (w) to the wavelength of the light (λ), the distance from the aperture to the screen (distance), and the width of the aperture (aperture width).

In this case, you are given that a bright patch of light with a width of 18.0 cm appears on the screen, which is located 2.00 m behind the aperture. However, you don't have the specific wavelength of light or the type of light mentioned.

To calculate the width of the diffraction pattern, you need to know the wavelength of light. Without this information, you won't be able to find the exact value. Different wavelengths of light have different behaviors and produce different patterns when passing through an aperture.

Also, the distance of the source of light being 4.00 m away from the aperture does not matter in this case. The distance of the source only affects the intensity or brightness of the light, but not the width of the diffraction pattern.

In summary, without knowing the wavelength of light or the type of light, you won't be able to calculate the exact value for the width of the diffraction pattern using the given equation.

The distance of the aperture from the light source only determines the intesnth, not the size of the bright "patch" of light on the other side.

It is customary to assume an average wavelength of visible light of 550 nm when no other wavelength infrmation is given.

What you can conclude from the information you have been given is the diameter of the aperture. You did not ask that question, however.

I believe the correct formula to use for the angular with of the light patch is
"Airey diffrection pattern" formula
theta = 1.22*(Lambda)/D
where lambda = 550*10^-9 m is
the wavelength

In your case, theta = 0.18/2 = 0.09 radians, so

D = 1.22*550*10^-9/0.09 = 7.6*10^-6 m
= 7.6*10^-3 mm
a quite small hole.