Image Formed by Lenses

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Software Engineer at Padandas

Published: 2024-01-01 Last updated: 2024-01-01

Image Formed by Lenses

A lens is an object, usually made of glass, bounded by one by two spherical surface. There are two types of lenses:

Convex or converging lens
Concave or diverging lens

A concave lens is thick at the thin centre and thin at the edges while a concave lens is thin at the centre and thick at the edges. A convex lens causes parallel rays of light to converge after refraction but the concave lens does the opposite. There are different types of lenses, shown in the figure.

Some related terms

Center of curvature:
The centre of the sphere of which lens forms a part is called the centre of curvature. A lens has two centres of curvature C₁ and C₂.
Radius of curvature:
The radius of the sphere whose parts form a lens is known as the radius of curvature. A lens consists of two radii of curvature R₁ and R₂ which may be equal.
Optical centre:
The geometrical centre of the lens is known as an optical centre. Here 'o' is the optical centre.
Principal focus:
When a parallel beam of light incident on a lens after refraction, it appears to meet from a point or it meet at a point. That point is called principal focus.
Note:Principal focus is real for the convex lens and virtual for the concave lens.
Principal axis:
The line passing through the centre of curvature of both spheres is called principal axis.
Focal length:
The distance between the optical centre and principal focus is called focal length.
Focal plane:
the plane passing through the focus and perpendicular to the principle axis of a lens is called the focal plane.

Image Formed by Lenses

Ray diagram are useful in locating the images formed by lenses. Any two of the following principle rays are sufficient to locate the image produced by the lens.

A ray passing through optical centre of the lens passes without deviation.
A ray parallel to the axis passes through the focus after refraction.
A ray passing through focus emerges parallel to the axis after refraction.

Image Formed by Convex Lens

When object lies at infinity
In this case, image will be formed in next side of the object at focus F which is real, inverted and point in size.
When object lies beyond 2F
In this case, image will be formed between F and 2F in the next side of the object which is real, inverted and smaller in size.
When object lies at 2F
In this case, image will be formed on next side of the object at 2F which is real, inverted and equal in size.
When object lies between F and 2F
In this case image will be formed in next side of object beyond 2F which is real, inverted and larger in size.
When object lies at F
In this case, image will be formed on next side of object at infinity which is real, inverted and highly magnified,
When object at F and O
In this case, image will be formed on the same side of the object which is virtual, erect and magnified.

Image Formed by a Concave Lens

When an object lies at any point on principle axis, it’s image formed by concave lens lies in same side of object which is virtual, erect and smaller in size.

Table showing formation of Images by lenses:

Lens	Position of object	Position of image	Nature of image	Size of image
Convex	1. At infinity	, At focus	Real and inverted	Extremely small
	2. Between infinity and 2f	Between infinity and 2f		Small
	3. At 2F	At 2F	Real and inverted	Small size
	4. Between 2F and F	Beyond 2F	Real and inverted	Magnified
	5. At focus	At infinity	Real and inverted	Extremely large
	6. Between focus and optical centre	On the side of object	Virtual and erect	Large
Concave	a. At infinity	At focus	Virtual and erect	Small
Concave	b. Between infinity and optical centre	Between focus and optical centre	Virtual and erect	Small

Action of a lens

A thin lens may be considered as made up of a large number of small angle prisms placed together. The refracting angle of these prisms, made by lens surfaces, increases from zero at the middle to a small value at the edges. The prism farther away from the middle deviates from zero an incident ray more than those prisms near the middle. A ray passing through the centre part of lens passes un deviated because it is a rectangular glass block. Such action of lens is shown in the figure.