Sign Convention for Spherical Mirror and Mirror Formula

 We have seen that using Ray Diagrams for Spherical Mirrors(Concave and Convex) we can determine the type of image formed by observing an object distance. But this doesn't give us the exact data that what is the size of the image formed? How much it's magnified or diminished? These things are found using Mirror Formulas. We will learn more about them but before that, we have to understand the sign convention method for a spherical mirror.

Sign Convention for Spherical Mirror

The Cartesian sign convention is used to determine whether the value we are taking for the calculation is positive or negative.

In mirrors, we need to calculate some things like

• Object distance (u)
• Image distance (v)
• Object height (h)
• Image height (h')
• Focal length (f)

Sign convention will help us to determine if this value is positive or negative, but before digging into sign convention we should understand what actually is the meaning of the above five.

What is Object Distance?

The distance of the object from the Pole is called object distance.

 It's denoted by u.

What is Image Distance?

The distance of the image formed from the Pole of the mirror is called image distance.

It's denoted by v.

What is the Focal length?

The distance between Pole and Focus is termed as Focal length.

It's denoted by f.

What is Object height and Image height?

It's meaning is the same as it says. One is the height of the object and another is the height of the image. Nothing special 😁

In the above diagram, you can see the sign convention. Here I've shown this using Concave Mirror. Your task will be to draw the same for the Convex Mirror. Don't panic you have to draw a simple graph sign convention (you use x-y axis to draw this) method but with a little twist. 

Get ready to see how I've drawn this sign convention diagram.

Important Principles 

• We'll take Pole of the mirror (both Concave and Convex) as the center.
• Distance towards the right of the pole will be Positive.
• Distance towards the left of the pole will be negative
• Distance above the Pole is Positive.
• The distance below the Pole is negative.
• You can see the distance above or below the Pole is nothing but the height of the image or object.
• The object is always placed on the left side of the mirror.
• The object is always placed above the Principal Axis.

The above note is very helpful. You can solve any question regarding this topic by understanding these and using your knowledge about basic parts of Mirror.

Now let's see what we're getting from the above principle.

Important notes

• Since the object is always above the Principal axis (distance above the pole) Object Height(h) will be always positive.
• Since the object is always placed towards the left side of the mirror, Object distance (u) will be always negative.
• If the image is formed above the principal axis then Image height(h') will be Positive. It means that the image is erect.
• If the image is formed below the principal axis then Image height(h') will be negative. It means that the image is inverted.
• If an image is formed on the left side of the mirror then the Image distance(v) is negative.
• If an image is formed on the right side of the mirror then the Image distance(v) is positive.
• Since the focus (F) of the Concave Mirror is on the left side of the mirror, focal length(f) is negative.
• Since the focus (F) of the Convex Mirror is on the right side of the mirror, focal length(f) is positive.

Mirror formula

The mirror formula is used to denote the relationship between object distance(u),  image distance(v), and focal length(f).

The relation is:-

1v+1u=1f

Magnification formula

It's the ratio of the height of the image(h') to the height of the object(h).

Magnification=Height of imageHeight of object

m=h'h