Derivation of Mirror Formula: Overview, Questions, Preparation

Few assumptions are taken into account while deriving the mirror formula which is listed below:

• It is assumed that the negative sign is the indication of the distance in the opposite direction and the positive sign indicates the distance in the same direction.
• The distance above the axis is positive, and the distance below the axis is negative.

I explained the derivation of the mirror formula below:

Let us assume that the object AB is at the distance of U from P, the pole of the mirror. And we can assume that the A1B1 points are formed at V from the mirror.

So, now we can say that:

∠ACB = ∠A1CB1

Now let us consider that the D and P points are close, we can write:

BC / B1C = PF / FB1

From this, we can say:

(PC – PB) / PB1 – PC = PF / (PB1 – PF)

Let us now substitute the values:

PC = -R

PB = u

PF = -f

PB1 = -v

Now, the equation is as follows:

(-R – (-u)) / (-v – (-R)) = -f / (-v – (-f))

(u – R) / (R – v) = -f (f – v)

(u – R) / (R – v) = f / (v – f)

After solving, we get

Uv – uf – Rv + Rf = Rf – vf,

Uv – uf – Rv + vf = 0,

We know that R = 2f,

So, Uv – uf – 2fv + vf = 0,

Uv – uf – vf = 0

 After solving it we get,

1 / v + 1 / u = 1 / f

As per the new pattern 2021, the chapter ‘Optics’ holds a weightage of 7 marks. It includes 2 questions in total, consisting of one short question of 2 marks and one long question of 5 marks.

Example 1) Illustrate the mirror formula.

Answer – The illustration is as follows:

Example 2) Write the equation of mirror formula

Answer – The formula of mirror formula is

1 / v + 1 / u = 1 / f

Here, u is the object distance,

V is the image distance,

And the f is the focal length.

Example 3) Write the meaning of R in the mirror formula.

Answer – The radius of the curvature in the mirror formula is denoted as R.

1) What do you mean by the Mirror formula?

2) What is the formula of a spherical mirror?

3) What is the Lens formula?

4) What is the SI unit of focal length?

5) What is the magnification formula for the mirror?