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A spherical mirror is a mirror whose reflecting surface is part of a sphere. Concave spherical mirrors have their reflective surface on the inner side, resembling a bowl, while convex mirrors have it on the outer side. In our exercise, we are dealing with a concave spherical mirror. These mirrors have specific properties, such as a center of curvature and a radius of curvature, both of which define the geometry of the mirror. The radius of curvature is the radius of the sphere from which the mirror segment is taken. It plays a critical role in determining the focal length, which is half the radius of curvature. Therefore, for a mirror with a radius of curvature of 22.0 cm, the focal length is calculated as \( f = \frac{22.0\, \text{cm}}{2} = 11.0\, \text{cm} \). Knowing the focal length helps us predict how the mirror will form images of objects placed in front of it.

The mirror equation provides a mathematical relationship between the object distance \( d_o \), the image distance \( d_i \), and the focal length \( f \) of a spherical mirror. The formula is given by \( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \). This equation is central to understanding how different factors affect the formation and characteristics of images. By substituting known values into the equation, one can calculate the missing variable.
In the case of our exercise, we have \( d_o = 16.5\, \text{cm} \) and \( f = 11.0\, \text{cm} \). Plugging these into the mirror equation allows us to solve for \( d_i \), which is the image distance. Rearranging the formula to \( \frac{1}{d_i} = \frac{1}{f} - \frac{1}{d_o} \), and calculating gives us an image distance of approximately 27.5 cm. A positive \( d_i \) implies that the image is real and located on the same side as the object.

A ray diagram is a practical tool for visually understanding how an image forms with spherical mirrors. It involves sketching principal rays to locate where they intersect, which determines the image position. For a concave mirror, common rays to draw include:

• A ray parallel to the principal axis, which reflects through the focal point.
• A ray passing through the focal point, which reflects parallel to the principal axis.
• A ray that goes through the center of curvature, reflecting back on itself.

These rays come together at a point to form the image of the object. In our example, the intersection indicates that the image forms on the same side of the mirror as the object, consistent with our findings using the mirror equation. This visual approach complements mathematical calculations, offering an intuitive grasp of image formation.

Image characteristics, such as position, size, orientation, and type, are key outcomes when studying image formation by spherical mirrors. Using the mirror equation and magnification formula, we can describe these features in detail. The image position is found to be 27.5 cm from the mirror’s vertex, indicating it's on the same side as the object, making it a real image.
The magnification \( m \) is calculated using \( m = -\frac{d_i}{d_o} \), which for this exercise results in \( m \approx -1.67 \). A negative magnification value implies that the image is inverted relative to the object. The size of the image \( h_i \) can be found by multiplying the magnification \( m \) by the object height \( h_o \), yielding \( h_i \approx -1.002\, \text{cm} \). Hence, the image is larger than the object, real, inverted, and located on the same side of the mirror.