Two Types of Image — Question 2

Question 2

Backward ray extensions identify a virtual image

Two outgoing rays travel in +x from x=0 and obey $y_1=2+0.20x$ and $y_2=-2-0.20x$, with coordinates in centimeters.

1. Find the intersection of their straight-line extensions and classify the image.

2. Find their separation at x=5 cm and determine whether any screen in the outgoing region can bring them to one point.

Question 2 - Solution

Backward ray extensions identify a virtual image

(a) Method and calculation

$$2+0.20x_I=-2-0.20x_I\Rightarrow\boxed{x_I=-10\,\mathrm{cm},\quad y_I=0}.$$$$x_I<0\Rightarrow\boxed{\text{virtual image from backward extensions}}.$$

(b) Interpretation and further calculation

$$\Delta y(x)=4+0.40x\Rightarrow\boxed{\Delta y(5)=6\,\mathrm{cm}}.$$$$x\ge0:\quad\Delta y(x)\ge4\,\mathrm{cm}>0\Rightarrow\boxed{\text{no outgoing screen focus}}.$$

Physical check

A virtual image remains visible to an eye or a later optical system; it simply is not a direct screen image in this outgoing region.