Lens Maker Formula

What is Lens Maker’s system?

The lens maker’s system is the connection among focal length, refractive index, and the radii of curvature used inside the lenses. The focal length is depending on the radii of the curvature and the refractive index. Manufacturers typically use this system for the producing cause of the lenses with their required optical instruments.

LENS MAKER SYSTEM

Lens makers are the relation between the focal length of a lens to the refractive index of its fabric and the radii of curvature of its surfaces. It is utilised by lens producers to make lenses of specific strength from the glass of a given refractive index. The lens is skinny, consequently, the gap measured from the poles of the 2 surfaces of the lens may be taken to be the same as the distances measured from the optical Centre.

The radius of Curvature and Focal Length of a Lens

A lens can encompass a couple of curved surfaces or an aircraft floor joined to a curved floor. The curved floor of a lens is a part of a sphere.

The radius of curvature: The radius of the glass sphere of which the floor of the lens is part is known as the radius of curvature of the given lens. Each lens has radii of curvature. With the extra width inside the form of a lens, there could be an extra width inside the radius of curvature.

Focal length : All the rays coming parallel to the principal axis of a lens, after refraction, both converge or seem to diverge from a factor at the principal axis known as the point of interest or principal focus. The distance between the optical centre and the point of interest of a lens is known as the focal length . A lens’s focal length varies with the refractive index of the fabric of the lens and the radii of curvatures of the 2 surfaces.

Sign conference

There is an indication conference that all of us should comply with even the use of the lens maker’s system. For refraction at a curved floor:

1. The distances measured alongside the route of the incident light are taken as positive, and the distances with the contrary route are negative.
2. The direction above the principal axis is taken to be positive, and the heights measured underneath the principal axis are taken as negative.

For convex lens:

R1:R1 – is positive

R2:R2 – is negative

f1:f1  – is positive

For concave lens:

R1:R1 – is negative

R2:R2  -is positive

f:f –  is negative

R1 & R2 is radius of curvature.

f is the focal length

Assumptions of the lens maker’s system

The assumptions of the lens maker’s system for the derivation are indexed underneath:

• Let us count on that the R1 & R2are the radii of the curvatures of the refracting surfaces.
• n1 & n2 are the refractive indices of the encircling medium.

Derivation of Lens maker system

Starting from the system of refraction, we have,

n2/v1-n2/u=n2-n1/R   ……… (Equation 1 for the primary floor)

n1/v-n2/v1=n1-n2/R2  ……… (Equation 2 for the second one floor)

After including the 1 and a couple of 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=(-1)(1/R1-1/R2)

Hence, the derivation of the lens maker system.

Limitations of the lens maker’s system

The boundaries of the lens maker’s system are as follows:

• For the space between refracting surfaces, the lens must be thin. 
• The medium wishes to be constant; inconsistencies on each side of the lens will not give desirable results.

CONCLUSION

The lens maker’s system defines a relation among the lens’s focal length , the refractive index of the fabric used to make the lens, and the radii of curvature of the 2 curved surfaces.  Lens producers often use it to make lenses of the desired focal length from glasses of various refractive indexes.

The focal length of the lens may be calculated if we’re given the values of the refractive index and the radius of the curvature of each the surfaces and the thickness of the lens, the use of the lens maker’s system as:

1/f=(-1)(1/R1-1/R2)