The linear magnification produced by a spherical mirror is -1.Analysing this value state the type of the mirror and position of the object with respect to the pole of the mirror. Draw the ray diagram to justify your answer.
To determine the type of the mirror and the position of the object with respect to the pole of the mirror, we need to analyze the given linear magnification value of -1. In optics, the linear magnification (m) is defined as the ratio of the height of the image (hi) to the height of the object (ho), represented as:
m = hi / ho
When the linear magnification is negative (-1 in this case), it indicates that the image formed by the mirror is inverted. In a spherical mirror, there are two types: concave and convex.
1. Concave mirror:
In a concave mirror, the reflecting surface is curved inward, and the reflecting surface faces towards the object. Concave mirrors can produce both real and virtual images, depending on the position of the object.
Since the linear magnification is negative (-1), the image formed by the concave mirror is real and inverted. This means that the object must be placed beyond the focal point (F) of the concave mirror, along the principal axis. The object distance (do) will be greater than twice the focal length (f) of the mirror.
2. Convex mirror:
In a convex mirror, the reflecting surface is curved outward, and the reflecting surface faces away from the object. Convex mirrors always produce virtual and diminished images.
Since the linear magnification is negative (-1), and the image formed by a convex mirror is always virtual and upright, we can conclude that the given linear magnification value of -1 is not possible for a convex mirror.
Therefore, based on the linear magnification value of -1, we can determine that the given mirror is a concave mirror. The object must be placed beyond the focal point of the concave mirror (F) along the principal axis.
To justify this answer, let's draw a ray diagram for a concave mirror with the object placed beyond the focal point:
Object (O)
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Principal Axis (P)
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F | F'
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Image (I)
In the ray diagram:
1. Draw an incident ray parallel to the principal axis, which appears to come from the focal point on the opposite side after reflection.
2. Draw another incident ray that passes through the center of curvature (C) of the mirror; it will be reflected back along the same path.
3. Finally, draw a reflected ray going through the focal point (F').
These two reflected rays will meet at a point on the principal axis, forming the inverted real image (I) of the object (O).
Thus, the concave mirror with the object placed beyond the focal point along the principal axis matches the given linear magnification value of -1, indicating a real and inverted image.