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When discussing concave mirrors, the mirror equation is a fundamental concept that helps us understand how mirrors form images. It is given by the formula: \( \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \). Here, \( f \) represents the focal length of the mirror, \( v \) is the distance from the mirror to the image, and \( u \) is the distance from the object to the mirror.
In practice, this equation allows us to relate the distances associated with image and object positions to find unknown values. By using the signs convention, where in concave mirrors the object distance is negative because it is measured against the direction of the incoming light, we can accurately solve real-world problems like determining the focal length.

The focal length of a mirror is a measure of how strongly it converges or diverges light. In a concave mirror, this length determines the radius at which parallel rays of light are focused to a point. The focal length \( f \) of a concave mirror is half the radius of curvature.
Knowing the focal length helps us predict how an image will form. In the exercise provided, by rearranging the mirror equation as \( f = \frac{1}{\frac{1}{v} + \frac{1}{u}} \), the calculated focal length is approximately -14.6 cm. The negative sign is crucial as it signifies that the mirror is concave, focusing the rays inwards.

Magnification in mirrors refers to how much larger or smaller an image appears compared to the actual object. It is described by the formula \( m = \frac{v}{u} \), where \( m \) is the magnification, and \( v \) and \( u \) are the image and object distances respectively.
In the given situation, the magnification is 1.4, meaning the image appears 1.4 times larger than the object. Understanding this concept helps to deduce not only the size but also the orientation of the image - in this case, an enlarged upright image since it appears on the same side of the mirror as the object.

Real images are formed when light rays actually converge at a point. For concave mirrors, real images are produced on the same side as the object when the object is placed beyond the focal point.
Real images are usually inverted, however, since our case involves a magnified direct image, the position must be carefully analyzed with measurements. The calculated image distance \( v = -35 \) cm indicates the image forms in front of the mirror, true to concave mirror behavior. This characteristic allows us to use the mirror for practical applications like shaving, where an enlarged and clear view is essential.