Two Types of Image — Question 7

Question 7

A converging incident bundle supplies a virtual object to a later element

Before reaching a second optical element at x=0, rays travel in +x and would meet at x=12 cm if that element were removed. Define its object distance p positive for an object on the incoming side. With the element present, outgoing rays meet at x=30 cm.

1. Assign the signed object and image distances for the second element.

2. Classify its object and image, and calculate the change in the convergence coordinate caused by insertion.

Question 7 - Solution

A converging incident bundle supplies a virtual object to a later element

(a) Method and calculation

$$x_{O,\mathrm{would\ be}}=+12\,\mathrm{cm}\Rightarrow\boxed{p=-12\,\mathrm{cm}}.$$$$x_{I,\mathrm{actual}}=+30\,\mathrm{cm}\Rightarrow\boxed{q=+30\,\mathrm{cm}}.$$

(b) Interpretation and further calculation

$$\boxed{\text{virtual object; real image}}.$$$$\boxed{\Delta x=30-12=18\,\mathrm{cm}}\quad\text{farther downstream}.$$

Physical check

The incoming rays do not originate from the virtual object point; they are already converging toward it when intercepted.