Cartesian sign conventions are used for measuring the various distances in the ray diagrams of spherical lenses. According to cartesian sign convention,
The object is always placed on the left side of the lens.
All the distances are measured from the optical centre of the lens.
The distances measured in the same direction as that of incident light are taken as positive.
The distances measured against the direction of incident light are taken as negative.
The distances measured upward and perpendicular to the principal axis is taken as positive.
The distances measured downward and perpendicular to the principal axis is taken as negative.
10th Science : Chapter 2 : Optics : Refraction Through a Convex Lens
REFRACTION THROUGH A CONVEX LENS
Let us discuss the formation of images by a convex lens when the object is placed at various positions.
Object at infinity
When an object is placed at infinity, a real image is formed at the principal focus. The size of the image is much smaller than that of the object.
Figure 2.6: Object at infinity
Object placed beyond C (>2F)
When an object is placed behind the center of curvature(beyond C), a real and inverted image is formed between the center of curvature and the principal focus. The size of the image is the same as that of the object.
Figure 2.7: Object placed beyond C (>2F)
Object placed at C
When an object is placed at the center of curvature, a real and inverted image is formed at the other center of curvature. The size of the image is the same as that of the object.
Figure 2.8: Object placed at C
Object placed between F and C
When an object is placed in between the center of curvature and principal focus, a real and inverted image is formed behind the center of curvature. The size of the image is bigger than that of the object.
Figure 2.9: Object placed between F and C
Object placed at the principal focus F
When an object is placed at the focus, a real image is formed at infinity. The size of the image is much larger than that of the object.
Figure 2.10: Object placed at the principal focus F
Object placed between the principal focus F and optical centre O
When an object is placed in between principal focus and optical centre, a virtual image is formed. The size of the image is larger than that of the object.
Figure 2.11: Object placed between the principal focus F and optical centre O
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A lens is an optically transparent medium bounded by two spherical refracting surfaces or one plane and one spherical surface.
Lens is basically classified into two types.
Primary Types of Lenses
They are:
(i) Convex Lens
(ii) Concave Lens
(i) Convex or bi-convex lens:
It is a lens bounded by two spherical surfaces such that it is thicker at the centre than at the edges. A beam of light passing through it, is converged to a point. So, a convex lens is also called as converging lens.
(ii) Concave or bi-concave Lens:
It is a lens bounded by two spherical surfaces such that it is thinner at the centre than at the edges. A parallel beam of light passing through it, is diverged or spread out. So, a concave lens is also called as diverging lens.
Other types of Lenses
Plano-convex lens:
If one of the faces of a bi-convex lens is plane, it is known as a plano-convex lens.
Plano-concave lens:
If one of the faces of a bi-concave lens is plane, it is known as a plano-concave lens.
All these lenses are shown in Figure 2.2 given below:
Figure 2.2: Types of lenses
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