Two Types of Image — Question 5

Question 5

Image orientation alone cannot distinguish real from virtual

Two optical stages each form a real image of their respective real object. Their transverse magnifications are m1=-2 and m2=-0.5. The first image serves as the real object for the second, which is placed farther downstream.

1. Find the final magnification relative to the original object.

2. For an original arrow 6 mm high, give the intermediate and final signed heights and classify the final image.

Question 5 - Solution

Image orientation alone cannot distinguish real from virtual

(a) Method and calculation

$$h_1=m_1h_0,\quad h_2=m_2h_1\Rightarrow\boxed{m_{\mathrm{total}}=m_2m_1=+1}.$$$$\boxed{h_1=-12\,\mathrm{mm}}.$$

(b) Interpretation and further calculation

$$\boxed{h_2=(-0.5)(-12)=+6\,\mathrm{mm}}.$$$$\boxed{\text{final image: real and upright relative to the original}}.$$

Physical check

Reality is determined by ray convergence at the last stage; upright orientation is a separate property measured relative to a chosen object.