Derivation of Gaussian formula forom particular situation

[Takuza]

Homework Statement

We are to derive the Gaussian formula for a case with a virtual object, a virtual image, and a concave surface.

Homework Equations

Snell's law, n(sin(phi)) = n'(sin(phi'))
geometry

The Attempt at a Solution

I can do a derivation for a situation with a point object placed to the left of a convex surface with a real image being formed, but I don't understand what it means to have a virtual object together with a virtual image, much less for a concave surface.

 

[anathema]

Can someone please explain this scenario in more detail?

Sure, I would be happy to explain this scenario in more detail. First of all, a virtual object refers to an object that does not physically exist but is created by the refraction of light rays. In this case, the virtual object would be located on the same side of the surface as the observer. Similarly, a virtual image is an image that is formed by the refraction of light rays but does not physically exist. The virtual image would be located on the opposite side of the surface from the observer.

Now, for the case of a concave surface, the surface curves inward, towards the observer. This means that the center of curvature, which is the center of the circle from which the surface is a part of, is located on the same side as the observer. Therefore, when light rays from the virtual object pass through the concave surface, they will diverge away from each other. This results in a virtual image being formed on the opposite side of the surface from the observer.

To derive the Gaussian formula for this scenario, you would use the same principles as you would for a convex surface with a real image. You would still use Snell's law to determine the relationship between the angles of incidence and refraction, but you would have to take into account the fact that the light rays are diverging rather than converging. This would result in a negative sign in the equation, indicating that the image formed is virtual.

I hope this helps clarify the scenario for you. Let me know if you have any further questions.