Introduction

Lenses are common items in our day-to-day lives, which are manufactured using glass or plastics. Today, the science behind it has become so advanced that scratch-resistant and lightweight plastics have taken over the market with significantly reduced costs.

It should be noted that designing a lens is a difficult and high-precision task no matter the raw material. The design should be such that its specifications are accurate. Apart from vision glasses, high-tech applications of lenses include cameras, telescopes, microscopes, etc. Today, the advent of optometry has brought about significant improvement in our lives, which cannot be summarized in just a few lines.

What is a Compound Lens?

A compound lens is manufactured by using two or more lenses so that light rays pass through all of them and each lens affects the image. The lens closest to the eye is known as the ocular lens or the eyepiece and the one closest to the object being viewed is known as the objective.

The purpose of a compound lens is to combine the powers of multiple lenses and allow for possibilities that wouldn’t have existed with a single lens.

Title: A microscope
Description: A microscope consists of multiple lenses to allow intense magnification.

Title: The objective lens of a microscope
Description: A microscope sometimes has multiple objective lenses and we can select which one we prefer to increase magnification.

In the images above, a microscope, which is a compound lens system, is shown. A closeup of the objective lens of the microscope is separately shown as well.

Formation Of The Compound Lens

If we consider a two-lens compound system like a microscope, it can be understood as follows: the objective lens forms an image of the object being viewed. This image becomes an object for the eyepiece, which further magnifies the image. Thus, the final image, seen via the eyepiece appears several times magnified, which wouldn’t have been easily achieved with a single lens.

Microscope

The Focal Length Of The Compound Lens

For a compound lens, the effective power is obtained by simply adding up the powers of the individual lenses. Suppose that these are represented by P1 and P2  and the lenses are named as L1 and L2 .

If the lenses are separated by a distance d, and f1 and f2 are the focal lengths of the individual lenses, then the formula for effective focal length is given as:

Advantages Of The Compound Lens

Using multiple lenses provides us with a number of advantages, chief among which are:

1. Using a highly specialized lens runs the risk of more defects and abnormalities. With multiple lenses, errors can be better managed.

2. The powers of a compound system are added up, which increases magnification as required.

Application Of The Compound Lens

Compound lenses are used in a large number of scenarios. Some of them are given below:

1. A simple microscope is made up of two convex lenses, which allow us to magnify the image of the object placed on the slide.

2. A telescope is also a compound lens system, which can magnify the image of far away objects.

These days, compound lenses are available in form factors as small as 2 mm. This is inspired by nature wherein, the insect eye consists of hundreds of small lenses in a  cluster. As many as 135 lenses in a single device have been manufactured which are used in car parking sensors, robots, printing, etc. Circuitry connected with this cluster can collate images from all the lenses and thus, generate a highly detailed view.

Eye of a fly

What Is Thin Lens?

A thin lens is made out of high-quality transparent optical material with a given radius of curvature. It is so called because the thickness is very small compared to its aperture. 

Focal Length Of Thin Lens

The figures given below show a convex and concave lens, respectively. If the thickness of the lens can be ignored with respect to its aperture, the focal length may be found as follows:

     

Let nL be the refractive index of the lens, and  nM  be the refractive index of the medium surrounding it. If R1 and R2 are the radii of the two curved surfaces of the lenses, the focal length is given by the following formula:

Use Of Thin Lens

Generally, the lenses used in telescopes and microscopes are thin lenses only since their size is large as compared to their thickness. Most handheld magnifiers, contact lenses, camera lenses, etc. can be treated as a thin lens.

Summary

This article explores thin lenses and compound lenses by discussing their principles, formulae, and various applications. It also provides an insight into determining the focal length when the radii of curvature of the surfaces of a lens are known. 

Image formation via a microscope is also explained, as well as an explanation of deriving the focal length of a compound system. The uses of lenses are discussed by taking optometry as an example.

Frequently Asked Questions

1. What is the nature of the focal length of thin lenses?

The two parameters have an inverse relation of sorts. Thick lenses have a higher ability to bend light rays and thus, have shorter focal lengths. On the other hand, thin lenses tend to have longer focal lengths.

2. What is the Newtonian form of lens equation?

Let x1 represent the object distance towards the left side of the lens and x2 be the image distance towards the right side of the lens. If f is the focal length, the Newtonian lens equation reads: 

3. What is nano printing of lens structure?

Nanoprinting is a manufacturing technology that can ready lenses within a few hours for use.

4. What is the aberration of lenses?

Aberrations are imperfections in the images formed by a lens. This happens when the image isn’t properly focussed and depending on the type of aberration, specific adjustments can be made.

5. What is the center of curvature of the lens? How is it related to focal length?

The center of the curved portion of the lens is known as the center of curvature of the lens. Its distance from the optical center is known as the radius of curvature, which is twice the focal length.