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Thin Lenses
A lens is conventionally defined as a piece of glass which is used to focus or change the direction of a beam of light passing through it.
They are mainly made of glass or plastic. Lens are used in making spectacles, cameras, cinema projectors, microscopes and telescopes.
Types of thin lenses.
A lens which is thicker at its centre than at its edges converges light and is called convex or converging lens.
A lens which is thicker at its edges than at its centre diverges light and is known as concave or diverging lens.
· Properties of lenses.
- Optical centre – this is the geometric centre of a lens which is usually shown using a black dot in ray diagrams. A ray travelling through the optical centre passes through in a straight line.
- Centre of curvature – this is the geometric centre of the circle of which the lens surface is part of. Since lenses have two surfaces there are two centres of curvature. C is used to denote one centre while the other is denoted by C1.
- Principal axis – this is an imaginary line which passes through the optical centre at right angle to the lens.
- Principal focus – this is a point through which all rays travelling parallel to the principal axis pass after refraction through the lens.
A lens has a principal focus on both its sides. F is used to denote the principal focus
- Focal length – this is the distance between the optical centre and the principal focus. It is denoted by ‘f’.
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The principal focus for a converging lens is real and virtual for a diverging lens.
It is important to note that the principal focus is not always halfway between the optical centre and the centre of curvature as it is in mirrors.
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Images formed by thin lenses.
The nature, size and position of the image formed by a particular lens depends on the position of the object in relation to the lens.
Construction of ray diagrams
Three rays are of particular importance in the construction of ray diagrams.
- A ray of light travelling parallel to the principal axis passes through the principal focus on refraction through the lens. In case of a concave lens the ray is diverged in a way that it appears to come from the principal focus.
- A ray of light travelling through the optical centre goes un-deviated along the same path.
- A ray of light travelling through the principal focus is refracted parallel to the principal axis on passing through the lens.
The construction of the rays is illustrated below.
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Images formed by a converging lens.
- Object between the lens and the principal focus.
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– Image formed behind the object
– Virtual
– Erect
– Magnified
- Object at infinity.
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– Image formed at the principal focus of the lens
– Real
– Inverted
– Diminished
- Object at the principal focus (at F).
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– Image is at infinity.
- Object between the principal focus (F) and 2 F.
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– Image situated beyond 2 F
– Real
– Inverted
– Magnified
- 5. Object at 2 F.
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– Image is formed at 2 F
– Real
– Inverted
– Same size as the object
- 6. Object beyond F.
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– Image moves nearer to F as object shifts further beyond 2 F
– Real
– Inverted
– Diminished
Images formed by a diverging lens.
Images formed by diverging lens are always erect, virtual and diminished for all positions of the object.
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Linear magnification.
The linear magnification produced by a lens defined as the ratio of the height of the image to the height of the object, denoted by letter ‘m’, therefore;
m = height of the image / height of the object.
Magnification is also given by = distance of the image from the lens/ dist. of object from lens. m = v / u
Example
An object 0.05 m high is placed 0.15 m in front of a convex lens of focal length 0.1 m.
Find by construction, the position, nature and size of the image. What is the magnification?·