Virtual source at the back of the mirror

[PintoCorreia]

Homework Statement

What is meant by this: "When mirroring a source in a plane mirror, it looks like the rebounding light rays come from a virtual source at the back of the mirror."

I will illustrate this with a question:

The figure shows a light source A, from
an ordinary light bulb, that
transmits rays in all directions. two
of those light rays (r1 and r2) are drawn
You also see a mirror. The (specular)
front you will find on the side of
the light source.
The drawing is a top view of
the situation, otherwise
said: we concentrate on
the directions in the plane in which we draw
and forget the space in which we
ourselves.

-The rebounding rays are portions of whole lines. Draw those entire lines, so
even the pieces on the back of the mirror and mark the point of intersection.-That marked point of intersection has a special position with respect to the light source!
What position is that? Show the validity of your claim.

Homework Equations

mirrors, Snellius

The Attempt at a Solution

Trying to understand...

What is meant by rays on the back of the mirror?

What type of 'special position' is meant here?

 

[ehild]

You know the law of reflection, draw some reflected rays, and extend the lines to the other side of the mirror. What do you see?


ehild

 

[PintoCorreia]

It feels a bit strange intuitively if you see that the blue line goes through the mirror, instead of bouncing off the mirror?

And what does the 'point of intersection' actually intersect? The mirror, the red line or what?

 

[ehild]

It feels a bit strange intuitively if you see that the blue line goes through the mirror, instead of bouncing off the mirror?

It bounces back from the mirror. The arrows show how the real light ray travels. But its line is extended behind the mirror.

And what does the 'point of intersection' actually intersect? The mirror, the red line or what?

If you take a second ray emerging from the source, and reflected from the mirror, the extension of that reflected ray intersects the extension of the first reflected ray. The extensions of all reflected rays intersect at a single point: That is the mirror image of the source point.

You see the object in the direction from where the light ray arrives to your eyes. It is a print-in knowledge in your brain that the light travels along straight lines. Your mind extends the light rays arriving to your eyes and "see" the object at the intersection of the extended lines.

Trace two rays emerging from the source. Choose one striking the mirror perpendicularly. Show geometrically how far from the mirror the intersection is.

ehild

 

[PintoCorreia]

Thanks. But What type of 'special position' is meant here?

 

[jtbell]

It means that there is a simple ("special") relationship between the locations of the object (source) and image (intersection of the extended rays behind the mirror). It's hard to say this more precisely without giving away the answer to the question.

When you make your own drawing for this, for best results, when you construct the rays, measure the angles as carefully as possible, and use a ruler or straightedge to draw the lines.

Also, I strongly suggest that you draw more than two lines from the object, at least three (r1, r2, r3,...) in different directions towards the mirror.

 

[CompuChip]

You see the object in the direction from where the light ray arrives to your eyes. It is a print-in knowledge in your brain that the light travels along straight lines. Your mind extends the light rays arriving to your eyes and "see" the object at the intersection of the extended lines.

I think you touched on something crucial there, ehild. There is no actual light ray going through the mirror, and your brain knows it, but still assumes that it does.

 

[PintoCorreia]

It means that there is a simple ("special") relationship between the locations of the object (source) and image (intersection of the extended rays behind the mirror).

You think this has an actual name?

"When you make your own drawing for this, for best results, when you construct the rays, measure the angles as carefully as possible, and use a ruler or straightedge to draw the lines." Yes, I know that there are 2 angles that are the same the angle between the incoming ray and the mirror and the ray between the reflected ray and the mirror. And you can draw a 'normal line' at that point.
But I don't see what is so special about this to come up with a name.

 

[ehild]

What is the position of the image? How far is it from the mirror ?

Look at your image in a mirror. What would you say where is it? (Opposite to you). Take a pen or pencil so as it goes from your eye to the image of the same eye (be careful do not hit your eye). See what angle does the pencil enclose with the mirror.

ehild

 

[PintoCorreia]

What is the position of the image? How far is it from the mirror ?

Look at your image in a mirror. What would you say where is it? (Opposite to you). Take a pen or pencil so as it goes from your eye to the image of the same eye (be careful do not hit your eye). See what angle does the pencil enclose with the mirror.

ehild

I guess you are suggesting a line of 180 degrees? Do you refer to the normal line?

 

[ehild]

Yes, the line connecting the source and the image is normal to the mirror. ehild

 

[PintoCorreia]

But do you mean the point of intersection has the same distance between the light source A and the reflected mirror image point A'?

 

[ehild]

But do you mean the point of intersection has the same distance between the light source A and the reflected mirror image point A'?

The point of intersection is the mirror image of A.

ehild