refraction

Lens

Lens is an optical device that is widely used in everyday life. Practically every adult wears a spectacle which is constructed out of lenses.
Lenses are classified according to the geometry and combination of the surfaces. Lenses are commonly used to form images by refraction in optical instruments such as cameras, telescopes, and microscopes.

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

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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.

1f = 1v−1u

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.

1. When the Object is Placed between F₁ and O:

Formation of Image by a Convex Lens
The image is -

• Formed on the same side of the lens

• Virtual

• Erect

• Magnified

2. When the Object is Placed between the Optical Center (O) and first Focus (F₁)

Here we consider two rays starting from the top of the object placed at F₁ and optical center. The ray parallel to the principal axis after refraction passes through the focus (F₂). The ray passing through the optical center goes through the lens undeviated. These refracted rays appear to meet only when produced backwards. Thus, when an object is placed between F₁ and O of a convex lens, a virtual, erect and magnified image of the object is formed on the same side of the lens as the object.

3. When the Object is Placed at 2F₁

The image is -

• Formed at 2F₂

• Real

• Inverted

• Same size as the object

Here one of the rays starting from the top of the object placed at 2F₁ passes through the optic center without any deviation and the other ray which is parallel to the principal axis after refraction passes through the focus. These two refracted rays meet at 2F₂. Thus, when an object is placed at 2F₁ of a convex lens, inverted and real image of the same size as the object is formed at 2F₂ on the other side of the lens.

4. When the Object is Placed between F₁ and F₂

The image is

• Formed beyond 2F₂

• Real

• Inverted

• Magnified

Let us consider two rays coming from the object. The ray which is parallel to the principal axis after refraction passes through the lens and passes through F₂ on the other side of the lens. The ray passing through the optic center comes out of the lens without any deviation. The two refracted rays intersect each other at a point beyond 2F₂. So, when an object is placed between F₁ and 2F₁ of a convex lens the image is formed beyond 2F₂.

5. When the Object is Placed at F₁

The image is -

• Formed at infinity

• real

• Inverted

• Magnified

Here again we consider two rays coming from the top of the object. One of the rays which is parallel to the principal axis after refraction passes through F₂ and the other ray which passes through the optical center comes out without any deviation. These two refracted rays are parallel to each other and parallel rays meet only at infinity. Thus, when an object is placed at F₁ of a convex lens, the image is formed at infinity and it is inverted, real and magnified.

6. When the Object is Placed beyond 2F₁

The image is -

• Formed between F₂ and 2F₂

• Real

• Inverted

• Diminished

The ray parallel to the principal axis after refraction passes through F₂ and the ray which passes through the optical center comes out without any deviation. The refracted rays intersect at a point between F₂ and 2F₂. The image is inverted, real and diminished.

7. When the Object is Placed at Infinity

The image is -

• Formed at F₂

• Inverted

• Real

• Highly diminished

When the object is at infinity, the rays coming from it are parallel to each other. Let one of the parallel rays pass through the focus F₁ and the other ray pass through the optical center. The ray which passes through F₁ becomes parallel to the principal axis after refraction and the ray which passes through the optical center does not suffer any deviation.

The table below gives at a glance the position, size and nature of the image formed by a convex lens corresponding to the different positions of the object and also its application.

Position of the object	Position of the image	Nature of the image	Size of the image	Application
Between O and F1	on the same side of the lens	Erect and virtual	Magnified	Magnifying lens (simple microscope), eye piece of many instruments
At 2F1	At 2F2	Inverted and real	Same size	Photocopying camera
Between F and 2F1	Beyond 2F2	Inverted and real	Magnified	Projectors, objectives of microscope
At F1	At infinity	Inverted and real	Magnified	Theatre spot lights
Beyond 2F1	Between F2 and 2F2	Inverted and real	Diminished	Photocopying (reduction camera)
At infinity	At F2	Inverted and real	Diminished	Objective of a telescope

Convex Lens Examples

 

The simplest example is the magnifying glass. The letters which are too small to read can easily be read by using a convex lens as a magnifying glass. The lens is held in such a way that the letters are within the focal length of the lens. Hence the letters are magnified and in upright position to make it easy to read. The same principle is used in spectacles which are used for correction of hyperopia. In olden days, convex lens were used to ignite by allowing the sun rays to be focused on the object to be ignited. Here the lens converge the heat rays just like converging the light rays.

Diverging Lens

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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.

When the Object is at Infinity: 

The image is -

• Formed at F₁

• Erect

• Virtual

• Diminished

When the Object is Placed between O and F:

The image is -

• Formed between O and F₁

• Erect

• Virtual

• Diminished

When the Object is Placed at any Position between O and Infinity:

The image is -

• Formed between O and F₁

• Erect

• Virtual

• Diminished

Convex Vs Concave Lens

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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.