Top

# Lens

Do you know why today's lenses are used instead of spectacle? Lens is a useful optical device which is now widely used in daily life and in place of spectacle. Lens has capacity for reflection of light and form a clear image. This is similar to mirror and used in various purposes and in optical instrument like telescope, microscope etc. it is formed with transparent material. It easily refracts light from its each boundary.

When a light strike on a lens then it gets reflected and at the same time, a beam of light has also existed from the lens. Due to this, a beam of light changes its direction. This is all because of its special geometry. Now we discuss what types of lenses, how they work to form an image, and the refraction process of converging and diverging lenses.

## Lens Definition

Lens is an optical device. It is formed by combination of two curved surfaces, mostly spherical surfaces with a common axis. It allows light and because of the curvatures and of the material of the lens it also gets refracted. Lenses are made of glass or transparent polycarbonate or transparent plastic materials. For the purpose of safety, polycarbonate materials are preferred for making lenses.

## Lens Types

Lenses are classified as per the types of surfaces used and also the combination of the surfaces. The shapes of common types of lenses are shown below.

A lens in which both the outer surfaces are concave outside the plane of lens is called a biconvex lens or simply convex lens. A lens in which both the outer surfaces are sunk inside the plane of lens is called a biconcave lens or simply concave lens. Of one of the surfaces of the lens is plain then it is either called a plano convex lens or a plano concave lens depending on what the other surface is.

## Lens Focal Length

The relationship between distance of the object (u), distance of the image (v) and focal length (f) of the lens is called lens formula or lens equation.
$\frac{1}{f}$ = $\frac{1}{v}-\frac{1}{u}$
This lens formula is applicable to both convex and concave lenses.

We said that the lens surfaces are spherical. The center of the spherical surface is called the center of curvature and its distance from the center of lens is called the radius of curvature. Half the radius of curvature is defined as the focal length of the lens. The point which is on the principal axis and away at a focal length from the lens is called ‘focus’ of the lens. This point is so called because the parallel rays that enter the lens converge (or deem to converge) together at this point.

Points to be remembered while using the lens formula. The values of the known parameters should be used with their proper sign as per the sign convention. No sign be assigned to the unknown parameter during calculations.

## Converging Lens

A biconvex lens or a plano convex lens converges parallel light rays that enter on one side to a point on the axis on the other side of the lens. Hence, a biconvex or a plano convex lens is called a converging lens. The point where the rays actually converge is called the focus of the lens and the distance of the focus from the lens is called focal length of the lens.

## Converging Lens Equation

The focal length, radius of curvatures of the surfaces and the refractive index of the material of a lens are all connected by an equation called as ‘lens maker’s equation’ or simply as ‘lens equation’. It is mathematically stated as,$\frac{1}{f}$ = $(n – 1)$ $[\frac{1}{R_{1}}–\frac{1}{R_{2}}+\frac{(n–1)d}{nR_{1}R_{2}}]$ Where,
$f$ = focal length
$n$ = refractive index of the material of the lens
$d$ = thickness of the lens
R1, R2 = Radius of curvatures of the respective surfaces.

Mostly, the thickness of the lens is neglected as it is much smaller compared to the radius of the surfaces and hence the lens equation for a thin lens can be approximated as,
$\frac{1}{f}$ ˜ $(n–1)$ $(\frac{1}{R_{1}}–\frac{1}{R_{2}})$

The normal convention is R1 and R2 is positive if the entering surface of the lens is concave and the other surface is convex. Both are negative if the surfaces are vice versa. Therefore the lens equation is, $\frac{1}{f}$ $\approx (n - 1)$ $(\frac{1}{R_{1}} – \frac{1}{R_{2}})$ for a converging lens. Diverging Lens Equation also same as converging lens.

## Diverging Lens

When a set of parallel rays enter a biconcave lens or a plano concave lens, it diverges the light rays on the other side of the lens. Hence, a biconcave or a plano concave lens is called a diverging lens. However these divergent rays give an impression that they emerge from a point on the axis at the same side of entry of the rays. It is a virtual point and not real. This point is called the focus and its distance from the lens is called focal length of the concave lens.

## Convex Vs Concave Lens

We have learned that the convex lenses converges the parallel rays to the focus on the other side of the lens. In other words, a ray of light parallel to the axis of the length will pass through the focus on the other side. A ray of light which passes through the optical center of the lens proceeds without any refraction. Hence the intersection of these two rays happens to be on the other side of the lens, there will be Real Image and inverted. But if the intersection do not actually occur on the other side and appears to intersect on the first side, then the image will be Virtual Image and upright.

But in case of concave lenses, the rays always get diverged and they can only ‘virtually’ intersect on the same side as the rays enter. Hence the images formed by concave lenses are always virtual images.
Let us make a table of comparison between these two lenses which can show the differences of their features side by side.

 Convex Lens Concave Lens The outer surfaces bulge out from the center line The outer surfaces shrink towards the center line Parallel rays that enter on one side get converged on the other side. Parallel rays that enter on one side get diverted on the other side. The focal length is positive. The focal length is negative. The images formed are real excepting when the object is within the focal length Only Virtual Images are formed in all cases. Images are inverted and form on the other side of the lens, excepting when the object is within the focal length Images (virtual) are always upright Mainly used in optical instruments and less used as corrective lenses in spectacles. Mainly used as corrective lenses in spectacles and less used optical instruments.

## Concave Lens

Concave lenses are also called as diverging lenses. Most of the adults have a deficiency called myopia, meaning near vision. They are helped in far vision by spectacles fitted with concave lenses.