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.
Let us discuss the formation of images by a concave lens when the object is placed at two possible positions.
Object at Infinity
When an object is placed at infinity, a virtual image is formed at the focus. The size of the image is much smaller than that of the object (Figure 2.12).
Figure 2.12 Concave lens-Object at infinity
Object anywhere on the principal axis at a finite distance
When an object is placed at a finite distance from the lens, a virtual image is formed between optical center and focus of the concave lens. The size of the image is smaller than that of the object (Figure 2.13).
Figure 2.13 Concave lens-Object at a finite distance
But, as the distance between the object and the lens is decreased, the distance between the image and the lens also keeps decreasing. Further, the size of the image formed increases as the distance between the object and the lens is decreased. This is shown in (figure 2.14).
Figure 2.14 Concave lens- Variation in position and size of image with object distance
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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Images Formed Due to Refraction Through a Convex and Concave Lens
When an object is placed in front of a lens, the light rays from the object fall on the lens. The position, size and nature of the image formed can be understood only if we know certain basic rules.
Rule 1:
When a ray of light strikes the convex or concave lens obliquely at its optical centre, it continues to follow its path without any deviation (Figure 2.3).
Rule 2:
When rays parallel to the principal axis strikes a convex or concave lens, the refracted rays are converged to (convex lens) or appear to diverge from (concave lens) the principal focus (Figure 2.4).
Rule 3:
When a ray passing through (convex lens) or directed towards (concave lens) the principal focus strikes a convex or concave lens, the refracted ray will be parallel to the principal axis (Figure 2.5).
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10th Science : Chapter 2 : Optics : Images Formed Due to Refraction Through a Convex and Concave Lens
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