Parallel and focal rays
Two easy rays: parallel to the axis, and through the focus.
Two helpful rays
To draw the image made by a mirror we need rays whose path after reflection is easy to know. A ray that runs parallel to the principal axis is one of them.
A ray parallel to the principal axis hits a concave mirror. Where do you think it goes after reflection?
What this lesson covers
The idea
A ray parallel to the principal axis, after reflection, passes through F of a concave mirror or appears to diverge from F of a convex mirror; a ray through (or directed towards) F emerges parallel to the principal axis.
Two helpful rays
To draw the image made by a mirror we need rays whose path after reflection is easy to know. A ray that runs parallel to the principal axis is one of them.
A ray parallel to the principal axis hits a concave mirror. Where do you think it goes after reflection?
- Through the principal focus F
- Back along the same path
- Away, parallel to the axis again
Concave and convex
Look at the red rays that come in parallel to the axis, and at the blue rays that go through (or towards) F. Open every tab.
Same two rules
Each rule works backwards too: a ray through F comes out parallel, and a parallel ray goes through F. For a convex mirror the same happens, but F is behind the mirror, so only the dashed extensions pass through it.
A ray parallel to the principal axis, after reflection, passes through F of a concave mirror or appears to diverge from F of a convex mirror. A ray through F of a concave mirror, or directed towards F of a convex mirror, emerges parallel to the principal axis.
Notes
A ray parallel to the axis goes through F (concave) or seems to come from F (convex). A ray through F (concave) or towards F (convex) comes out parallel to the axis.
Check yourself
A ray parallel to the principal axis falls on a concave mirror. After reflection it
A ray parallel to the principal axis falls on a convex mirror. After reflection it
Which ray emerges parallel to the principal axis after reflection from a concave mirror?
A ray is directed towards the focus F of a convex mirror, which is behind the mirror. After reflection it
- passes through the principal focus F — correct. Yes!
- returns along the same path. A ray returns along the same path only if it falls along the normal, as a ray through C does.
- goes on parallel to the axis. A ray that comes out parallel is one that passed through F before reflection. A parallel ray goes through F.
- passes through F in front of the mirror. The focus of a convex mirror is behind the mirror, so the reflected ray only appears to come from it.
- appears to diverge from F, which is behind the mirror — correct. Yes!
- comes out parallel to the axis. A convex mirror turns a parallel ray away from the axis. The ray appears to come from F.
- A ray striking the pole obliquely. A ray that strikes the pole obliquely is reflected obliquely, making equal angles with the axis.
- A ray travelling parallel to the axis. A parallel ray is reflected through F, so it does not stay parallel to the axis.
- A ray passing through F — correct. Yes!
- emerges parallel to the principal axis — correct. Yes!
- returns along the same path. Only a ray directed towards the centre of curvature comes back along the same path.
- passes through the pole. A ray directed towards F is reflected at the mirror surface and then runs parallel to the axis.