Finding an image with two rays

The idea

Each point of an extended object acts as a point source; its image lies where at least two reflected rays, chosen so that their directions after reflection are easy to know, intersect.

One point of a candle

Think of the tip of a candle flame as a tiny lamp that sends light in all directions towards a concave mirror. We want to find where the mirror makes the image of that tip.

How many reflected rays do we need to find the place of the image of the tip?

• Two rays, whose reflected paths cross
• Just one ray
• Every ray that leaves the tip, drawn one by one

Build the diagram

Press Next step and watch how the image of the top point is found, and then the whole image.

Where the rays cross

Many rays from T met again at one point after reflection. Two of them are enough to find it.

Each point of an extended object acts like a point source. Its image lies where at least two reflected rays intersect. We choose the rays so that their directions after reflection are easy to know.

Notes

The image of a point is where at least two reflected rays cross. We pick the two rays whose paths after reflection are easy to know.

Check yourself

How do we treat each small portion of an extended object in a ray diagram?

What is the least number of reflected rays that must intersect to give the position of the image of a point?

Why do we pick rays like the one parallel to the axis and the one through F?

In the last pictures, where is the image of the tip of the object?

• As a screen that catches the image. A screen is only used to catch a real image. Each portion of the object itself sends out light, like a point source.
• As a part of the mirror. The object is separate from the mirror. Each portion of it acts like a point source.
• As a point source that sends out rays in all directions — correct. Yes!
• Two — correct. Yes!
• One. One ray gives only a line. The image is where at least two reflected rays intersect.
• Four. Four is more than needed. Two reflected rays are enough, and fewer rays keep the diagram clear.
• Because they are the only rays that leave the object. An infinite number of rays leave each point of the object. We pick these two because it is easy to know their directions after reflection.
• Their directions after reflection are easy to know — correct. Yes!
• Because other rays are not reflected by the mirror. All the rays are reflected and follow the laws of reflection. These two are chosen for convenience.
• At the pole of the mirror. The rays cross at the image point, not at the pole. Both rays do touch the mirror, but they meet again after reflection.
• At the tip of the object. The tip of the object is the point source. The reflected rays cross at a different place, where its image is.
• Where the two reflected rays cross — correct. Yes!