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# Convex Lens

An optical device lens is very useful for reflecting and transmitting light. It is also useful for converging and diverging process. It is made up with transparent material which can reflect light to form an image. Lenses can be described as small refracting prisms which can be formed a clear image at a point.

Different types of lenses are converging and diverging lenses. These are differed in shape and their material. The converging lenses are the one which are used for light converging which is in parallel to principle axis. These can be identified by their specific shape because these have thin edges while thick mid part. But the diverging lens is used for diverging light and thick from the edges while thin in mid parts. A microwave lens is made up with paraffin wax which can reflect electromagnetic radiation. Let’s discuss convex lens which comes in the category of a converging lens.

## Convex Lens Definition

Generally optical lenses are made of two curved surfaces, mostly spherical. If those surfaces concave outside the plane of the lens, then the lens is called as convex lens. A convex lens can converge a beam of parallel rays to a point on the other side of the lens. This point is called as focus of the lens and its distance from the Optical Center of the beam is called the focal length. The radii of curvatures R1 and R2 of the spherical surfaces and the focal length of the lens ‘f’ are connected by an approximate equation, called lens makers equation.

It is stated mathematically as,

$\frac{1}{f}$ ˜ $(n – 1)$$(\frac{1}{R_{1}}–\frac{1}{R_{2}})$

where ‘n’ is the refractive index of the material of the lens.

If both the surfaces are curved and concave outside, then the lens is called Biconvex lens or Double Convex Lens or simply called as ‘convex lens’. In case of Double Convex Lens, the focal length is greater due to the presence of second curved surface. Since many optical devices require longer focal lengths, Double Convex Lenses are more preferred in use.

As mentioned earlier a convex lens with one surface as plain is called as Plano Convex Lens. Obviously the radius of curvature for the plain side is infinity. Therefore, when compared to a Double Convex Lens of the same material, the focal length is smaller for a Plano Convex Lens. This fact is made useful for making spectacle lenses of higher powers (lower the focal length, higher the power of the lens).

## Convex Lens Ray Diagram

When an object is placed in front of a lens, light rays coming from the object fall on the lens and get refracted. The refracted rays produce an image at a point where they intersect or appear to intersect each other. The formation of images by lenses is usually shown by a ray diagram. To construct a ray diagram we need atleast two rays whose path after refraction through the lens is known. Any two of the following rays are usually considered for constructing ray diagrams.
• A ray of light passing through the Optical Center of the lens travels straight without suffering any deviation. This holds good only in the case of a thin lens.
• An incident ray parallel to the principal axis after refraction passes through the focus.
• An incident ray passing through the focus of a lens emerge parallel to the principal axis after refraction.

The nature of images formed by a convex lens depends upon the distance of the object from the Optical Center of the lens. Let us now see how the image is formed by a convex lens for various positions of the object.

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