Concave Mirror – No Parallax

Parallax is the term used to describe the error in position of objects due to their relative position to us. To illustrate this, I need you to do a little demo at home for me. Firstly, hold the index finger of your left hand near your face and hold the index finger of your right hand as far away as you can reach. Now move your head slowly left and right whilst keeping your fingers stationary (this is easiest to do if you focus on the finger that’s far away). Hopefully you’ll observe that the finger closest to you appears to “run past” the finger that’s further away – as you move your head left, the close finger will “run” past the distant finger to the right, and the opposite will happen when you move your head to the right. This is because your fingers are in different positions relative to your head and therefore they have parallax.

The way to get your fingers to have “no parallax” is to put them side-by-side so that they move at the same speed as each other.

This reveals two important features of the “no parallax” test:

• No parallax is only evident when both objects are moving at the same speed
• No parallax is only evident when both objects are in the same location

To utilise this principle to help us locate the centre of curvature of a concave spherical mirror, we need to place an object (e.g. a pin) facing the reflective side of the mirror, as demonstrated below.

Now in order to locate the centre of curvature and therefore, be able to measure the distance of the radius of curvature, we need to get the object (the real pin) and the image of the pin to be in the same location. This is because with positiviely powered mirrors, when an object is placed at the centre of curvature, the image forms in the same location, but inverted.

But how do we determine where the location of the image in the mirror is? Well, this is where the “no parallax” test will prove to be useful. We know that if an object and an image have “no parallax” (i.e. they appear to be moving at the same speed as each other) then they must be in the same location. All we have to do then is put ourselves behind the pin so that we can view both the real pin and the image of the pin (as reflected through the mirror) and move our head left-right to see how the object and image move relative to one another.

We would then adjust the pin by moving it forwards or backwards until the object and image moved at the same speed, just like in the video below. This is the point of “no parallax”!