Thin Lenses

Lenses are curved, 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. You must be familiar with magnifying glasses. A single convex lens with a frame makes up a simple magnifying glass. Lenses, such as spectacles and contact lenses, are used to correct vision problems such as hypermetropia (long-sightedness) and myopia (nearsightedness or short-sightedness).

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 and is provided by the following formula:

1/f = 1/f1 + 1/f2 

f, combined focal length

f1, the focal length of the first lens

f2, the focal length of the second lens

Since power is the reciprocal of focal length, what is very obvious in this case? 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

While dealing with the combination of lenses or compound lenses, you may come across the following terms.

Combination of thin contact lenses

Once two lenses are combined, the primary forms a picture that then is an object for the second lens. This can be the final image made by the combination of lenses. Think about two lenses, A and B, with focal lengths f1 and f2 placed in contact with each other. Since the lenses are thin, we tend to assume that the optical centers of the lenses coincide. The primary lens produces an I1 image. Since image I1 is real, it is a virtual object for the second lens B, manufacturing 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. 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.

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,

1p–1q= 1f (lens formula)

where,

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

Determining power of a lens using the lens formula

Definition: 

Power of a lens is defined as the reciprocal of focal length in metres.

Mathematically,

P  =  1/f

In terms of lens formula, we can write as,

P=1p–1q

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

Determining magnification of the lens using lens formula

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

    M   =   u/v

Here u object distance and v is image distance.

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.