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Light - Part IV |
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Case
2 : Image formed by a concave mirror when the object is placed at the focus F. Consider
the following figure. Let
the object be a candle AB at F. Consider
two rays of light from point A. AD is parallel to the principal axis CP, and
AE passing through C. From rule 1 and 2, we see that ray of light AD will be
reflected along DFY, passing through the focal point F. D is the point of
reflection on MMí. Similarly ray CAE will be reflected at point E on MMí
and will return along EAC itself. The
two reflected rays are parallel to each other and will meet at infinity!!
Thus the image of point A will be at infinity. You can also see that the
image of A will be on the opposite side of the principal axis CP, hence the
image is also inverted besides being formed at infinity. As you extrapolate
the two lines, you will see that the image of A will be highly magnified.
The image of B will be fall on the line CP itself (rule 2). Thus
we can conclude that for an image of an object placed at the focus F of a
concave mirror :
Case
3 : Image formed by a concave mirror when the object is placed between the
focus F and the centre of curvature C. Consider the following figure. Let
the object be a candle AB placed between F and C. Consider
two rays of light emanating from point A. AD is parallel to CP. D is the
point of reflection on MMí. AD is reflected along DFAí (rule 1). The
second ray of light AE is cutting the principal axis CP at C. Hence by rule
2, the reflection of AE at a point E on MMî will be along EAC itself.
Lines DFAí and EAC meet at Aí, which is the reflected image of A.
Again, as explained earlier, light from B will go un-deflected along
PBC path. The image of AB is AíBí. Clearly the image is magnified and
inverted. Thus
we can conclude that for an image of an object placed between focus F and
the centre of curvature C of a concave mirror :
Case
4 : Image formed by a concave mirror when the object is placed at the centre
of curvature C. Consider the following figure. Let
the object be a candle AB placed at C. As
before, consider two rays emanating from A; one AD is parallel to CP the principal
axis. The second ray is AFE passing through focal point F. From
rule 1, we see that ray AD will be reflected at point D on MM' and pass
through the focal point F. The reflected ray is thus DFAí. The second ray
AFE, from rule 3, will on reflection at E, become parallel to the principal axis CP. The reflected ray is now EAí. EAí is parallel to CP. Again, as
explained earlier, light from B will go un-deflected along PBC path. The
image of AB is AíBí. Clearly the image is un-magnified and inverted and
is formed at C itself. Thus
we can conclude that for an image of an object placed at the centre of
curvature C of a concave mirror :
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