# Derivation Of Lens Maker Formula

For various optical equipment, lenses of varying focal lengths are utilized. The focal length of a lens is determined by the refractive index of the lens's material and the curvature radii of the two surfaces. The derivation of the lens maker formula is offered here to help applicants better comprehend the subject. The lens maker formula is often used by lens manufacturers to create lenses with the appropriate focal length.

## Lens formula or lens equation or define lens formula or definition of lens formula or state lens formula or what is lens formula?

For spherical lenses, the lens equation or lens formula is an equation that links the focal length, image distance, and object distance.

Lens Formula = is how it's written. where. v is the image's distance from the lens, u is the object distance and f is the focal length.

## What is lens making formula? Or state lens making formula or define lens making formula or define lens making formula:-

Concave and convex. The relationship between a lens' focal length, the refractive index of its material, and the radii of curvature of its two surfaces is known as the lens maker's formula. Lens manufacturers utilize it to build lenses with a specific power from glass with a specific refractive index.

Focal length-

The focal length of an optical system is the inverse of the system's optical power; it measures how strongly the system converges or diverges light. A system with a positive focal length converges light, while one with a negative focal length diverges light.

What is thin lens?A thin lens is defined as one whose thickness is insignificant in comparison to its curvature radii. The thickness (t) is significantly lower than the two curvature radii R1 and R2.

The focal length, image distance, and object distance are all connected in the lens formula for concave and convex lenses. The formula 1/f = 1/v + 1/u can be used to establish this link.

The focal length of the lens is f, and the distance of the generated image from the lens' optical center is v in this equation. Finally, u is the distance between an item and the optical center of this lens. For convex lenses, this is the lens equation.

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There are two types of thin lenses-

To create a thin lens formula, you must first understand the difference between converging and diverging lenses.

1. Converging lenses allow light rays that are parallel to the optic axis to pass through and converge at a common point behind them. The focal point (f) or focus is the name given to this point.
2. Diverging - These lenses have the opposite purpose as converging lenses. Light rays parallel to the optic axis travel through and diverge here. It creates an optical illusion by giving the impression that the lights are coming from the same source (f) in front of the lens.

What is formula of focal lens?The formula (1/v) + (1/u) = (1/f) gives the focal length of a double convex lens, where u is the distance between the object and the lens and v is the distance between the image and the lens.

OR

F = -R/2

Where,

F is focal length,and

R is radius of curvature of lens

## Derivation of lens maker’s formula-

The lens maker formula is derived using the assumptions listed below.

• Consider the thin lens in the picture above, which has two refracting surfaces with curvature radii R1 and R2, respectively.

• Assume that the surrounding medium and the lens material have refractive indices of n1 and n2, respectively.

The whole derivation of the lens maker formula is provided further below. We can say that, using the formula for refraction at a single spherical surface,

For the first surface,

For the second surface,

Now adding equation (1) and (2),

n1/v -n1/u = (n2-n1)[1/R1 - 1/ R2]

on simplifying we get,

1/v- 1/u = (n2/n1 -1) [ 1/R1- 1/R2]

When u = ∞ and v = f

But also,

Therefore, we can say that,

Where μ is the material's refractive index.

This is the derivation of the lens maker formula. Examine the constraints of the lens maker's formula to have a better understanding of the lens maker's formula derivation.

Image formation with a thin lens : characteristics

It's not enough to know the thin lens formula for convex lenses. The characteristics of a ray of light going through converging and diverging lenses must be understood.

1. On the opposite side, parallel rays going through converging lenses will intersect at point f.
1. Parallel rays seem to emerge from point f in front of diverging lenses.
1. The direction of light rays travelling through the centre of converging or diverging lenses does not change.
1. Light rays that enter a converging lens through its focal point always exit parallel to the lens's axis.
1. On the other side of a diverging lens, a light ray going towards the focal point will also emerge out parallel to its axis.

A concave or divergent lens has a negative focal length. When the picture is generated on the side where the object is positioned, the image distance is also negative. The image is virtual in this case. A converging or convex lens, on the other hand, has a positive focal length.

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