Two Types of Image — Question 1

Question 1

Measured outgoing rays locate a real image without identifying the optical element

Beyond an optical device, light travels toward increasing x. Two rays obey $y_1=3.0-0.10x$ and $y_2=-1.0+0.10x$, with x and y in centimeters. The output plane is x=0.

1. Locate their common image point and classify it.

2. Find the ray separation on a screen at x=15 cm and the screen displacement required for focus.

Question 1 - Solution

Measured outgoing rays locate a real image without identifying the optical element

(a) Method and calculation

$$3.0-0.10x_I=-1.0+0.10x_I\Rightarrow\boxed{x_I=20\,\mathrm{cm}}.$$$$\boxed{y_I=1.0\,\mathrm{cm}};\quad x_I>0\Rightarrow\text{real image}.$$

(b) Interpretation and further calculation

$$\Delta y(15)=|1.5-0.5|=\boxed{1.0\,\mathrm{cm}}.$$$$\boxed{\Delta x_{\mathrm{screen}}=20-15=+5\,\mathrm{cm}}.$$

Physical check

The rays physically reach the intersection after leaving the device, so a screen can intercept the focused light.