Derivation of Lens Maker Formula: Overview, Questions, Preparation

The lens maker's formula is the relationship between focal length, refractive index, and the radii of curvature used in the lenses. The focal length is dependent on the radii of the curvature and the refractive index. Manufacturers usually use this formula for the manufacturing purpose of the lenses with their required optical instruments.

The assumptions of the lens maker's formula for the derivation are listed below:

• Let us assume that the R1 and R2 are the radii of the curvatures of the refracting surfaces.
• N1 and n2 are the refractive indices of the surrounding medium.

Starting from the formula of refraction, we have,

N2 / v1 - n2 / u = n2 – n1 / R ……... (equation 1 for the first surface)

N1 / v - n2 / v1 = n1 – n2 / R2 ……… (equation 2 for the second surface)

After adding the 1 and 2 equations together, we get

N1 / v – n1 / u = (n2 / n1) (1 / R1 – 1 / R2)

= 1 / v – 1 / u = (n2 / n1 – 1) (1 / R1 – 1 / R2)

Here, u = ∞ and v = f

1/ f = (n2 / n1 – 1) (1 / R1 – 1 / R2)

 Also, 1 / v – 1 / u = 1 / f

We can say that,

1 / f = (u – 1) (1 / R1 – 1 / R2)

Hence, the derivation of the lens maker formula.

The limitations of the lens makers formula are as follows:

• The lens needs to be thin for the space of refracting surfaces. A thick lens doesn't work better.
• The medium needs to be the same; inconsistent mediums on both sides of the lens will not work. 

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) Write the equation of the lens maker formula.

Answer – The equation of the lens makers formula is 1 / f = (u – 1) (1 / R1 – 1 / R2)

Example 2) Write the equation of the 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 assumptions used for the derivation of the lens maker formula.

Answer – The assumptions of the lens maker's formula for the derivation are listed below:

• Let us assume that the R1 and R2 are the radii of the curvatures of the refracting surfaces.
• N1 and n2 are the refractive indices of the surrounding medium.

Question 1) What do you mean by the Lens maker formula?

Question 2) What type of lens is used for a human eye?

Question 3) what are the R1 and R2 in the lens maker formula?

Question 4) What are the limitations of the lens maker formula?

Question 5) What are the major types of lenses?