Lens Formula

Introduction

In General ray drawings can be used to determine the location of the image, the size, shape and type of the image built of objects when placed somewhere in front of the lens. Ray drawings provide useful information about image-object relationships, yet fail to provide information in the quantitative form.

While a ray diagram may help one to determine the approx. position and size of the image. It will not provide numerical information about the distance to the image and image size. For this type of numerical information, it is necessary to use the Lens Equation and the Magnification Equation which is also known as Lens Formula.

Object Distance

In General the distance of an object from the optical center of the lens is known as object distance. It is denoted or represented by u.

Image Distance

The distance of the image from the optical center of the lens is known as the Image Distance and it is denoted by the symbol v.

Focal Length

Focal Length is expressed as the distance of the principal focus from the optical center of the lens is called focal length. It is represented by f.

Light Lens Formula

In General the Relation between distance of object, image distance and focal length for a lens is called lens formula.

1v–1u=1f

Where, v is the image distance

U is the object distance and f is the focal length. Basically the distance of the object and image is measured from the center of the lens. The value or sign depends upon the convention.

Generally this lens formula is accepted or true for all situations for spherical lenses. Here, if we know any two values we are able to calculate the third one.

Magnification

Magnification is generally expressed or determined as the ratio of height of the image and that of the height of the object or we can say that height of image and distance of object is also known as Magnification. It is represented by ‘m’

i.e.                                                             m=Height of Image h’Height of object

      Or 

m=Height of Image vDistance of Object u

Here in this case:

Positive sign of magnification shows that the image is erect and virtual.

Negative sign of magnification shows that the image is real and inverted.

Power of a lens

In General a convex lens with short focal length converges the light ray with greater degree nearer to principal focus and a concave lens having short focal length diverges the light rays with greater degree nearer to principal focus.

The degree of divergence and convergence of rays of light by a lens is expressed in terms of the power of the lens. In general the degree of convergence and divergence depends upon the focal length of a lens. Basically it is denoted by ‘p’. The power of a lens is reciprocal of the focal length.

i.e. Power=1Focal length

p=1f

The SI unit is diopter and is denoted by ‘D’.

Generally, a convex lens has power in positive and the concave lens has power in negative.

Cartesian sign Convention

• All the diagrams are drawn by considering light traveling from left to right.
• All the distances are measured from a reference surface. Distance to the left to the surface are negative
• In General the distance of a real object is negative.
• Basically the distance of a real image is positive.
• Height above the axis is considered as positive.
• Angles which are measured clockwise from the axis are negative.

Lens Maker Formula

Real lenses have a limited thickness between their two surfaces of curvature. An ideal thin lens with two surfaces of equal curvature will have generally zero optical power. It means that it will neither converge nor diverge light. A lens with some thickness which is not negligible is called a thick lens.

Lenses are two types based on the curvature of two surfaces. Convex and concave.

The lens maker formula is the relationship between the focal length of the lens to the refractive index of its object and the radius of the curvature of its two surfaces. It is used by lens manufacturers to make specific power lenses from a given refractive index.

The lens is thin, so the distance measured from the poles of the two surfaces of the lens can be taken to match the distances measured from the optical center.

The lens maker formula is used to create a lens with a specified focal length. The lens has two curved surfaces, but they are not exactly the same. If we know the refractive index and the radius of curvature of both the surface then we can determine the focal length of the lens using the lens maker formula provided:

Lense Maker Formula=1f=μ-1×(1R1–1R2)

Where, f=Focal length of lens

μ= Refractive index

R1and R2= Radius of curvature of both surface

Conclusion

The lens is an open or transparent source bound by two surfaces and at least one of the two must be curved. A lens is said to be thin if the gap between the two surfaces is too small. In general a lens will be converging with positive focal length, and diverging if the focal length is negative.

So in this case, we can conclude that the convex lens does not need to be a converging lens and concave to diverging. Each lens has a value that we can determine by using a lens maker formula. This article will explain these examples.