Combination of thin lenses in contact

Lenses are curved and transparent objects that refract light. Convex lenses (bulging outward, converging light rays) and Concave lenses (bulging inward, diverging light rays) are two types of lenses. Cameras, binoculars and telescopes all employ lenses. Lenses such as spectacles and contact lenses are used to correct vision problems such as hypermetropia (long-sightedness) and myopia (nearsightedness) (short-sightedness). Besides, a single convex lens with a frame makes up a simple magnifying glass. 

Combination of thin lenses

Compound lenses are the type of lenses that have two thin lenses mounted on a common axis that are generally closer to each other or often glued together.

The following formula gives the common focal length for a system, where two subtle lenses sharing an axis are maintained in contact with each other:

1/f = 1/f1 + 1/f2 

Where

f =  combined focal length

f1 = the focal length of the first lens

f2 = the focal length of the second lens

For thin contact lenses, it is quite evident that the system’s combined power is given by the sum of the powers of the individual lenses.

But what if the lenses aren’t in contact with each other? If the lenses are separated by a distance “d”, then, in this case, the combination of focal length can be calculated using the following formula.

1/f = 1/f1 + 1/f2 – d/f1.f2

Combination of thin contact lenses

Once two lenses are combined, the primary lens forms an image then this image will be an object for the secondary lens.. The final image is made by the combination of lenses. Think about two lenses, A and B, with focal lengths f1 and f2 placed in reality with each other. Since the lenses are thin, we tend to assume that the optical centers of the lenses coincide. 

Let this central purpose be denoted by P. The primary lens produces an I1 image. Since image I1 is real, it is a virtual object for the second lens B, resulting in the ultimate image at I. However, it is essential to remember that the primary lens is likely to generate an image only to aid in determining the position of the final image. The direction of rays rising from the first lens gets changed in accordance with the angle at which they strike the second lens.

Lens Formula 

The lens formula is an equation that shows the relationship between focal length, object distance and image distance.

• The lens formula is for lenses with very thin thickness.
• Both convex and concave lenses are affected by the lens formula.
• The Lens-Maker’s Formula is used to create the lens formula.
• The focal length of the lens is determined using the lens formula.

Mathematically, 

The reciprocal of a lens’s focal length is equal to the sum of its object and image distance reciprocals.

It is given by,

 1/p + 1/q    =  1/f

(thin lens formula)

where,

p = object distance
q = image distance
f  = focal length of the lens

Determining Power Of A Lens By Using Lens Formula

The reciprocal of focal length in meters is the power of the lens.

Mathematically,

P  =   1 /f
        

In terms of thin lens formula, we can write this as,

P  =   1/p + 1/q
        

Unit: The unit of power of the lens is m-1 or diopters.

Determining Magnification Of The Lens By Using Lens Formula

The ratio of the height of the image created to the height of the object is the magnification of a lens. Magnification        

    M   =   v/u

or,     M  =   q/p.

Hence, another definition of magnification is the ratio between image distance and the object distance. As it is a ratio, magnification has no unit.

Conclusion :

Such a lens aggregation machine is normally used in the design of lenses for cameras, microscopes, telescopes and various optical instruments. The lens aggregate  is commonly used in arranging the lenses of microscopes, cameras, telescopes and various optical instruments.Nature has endued with the human eye (retina) with the sensitivity to sight magnetism waves during a little vary of the electromagnetic spectrum. The radiation happiness to the current region of this spectrum (wavelength of concerning four hundred nm at 750 nm) is named light. It’s primarily through light and therefore the sense of sight that we all know and interpret the planet around us. 

As we know, we need to use the lens maker’s method to clear up this query. Along with this, we need to clean approximately the situations of chromatic aberration and achromatic aggregate. Also, the above query is a typical piece. So, try and be careful in doing the calculations. An aggregate of lenses is used to boom the sharpness of the photo, to boom the magnification of the photo, to make the very last photo erect.