A beautiful girl with two normal eyes wants to see full...

A beautiful girl with two normal eyes wants to see full width of her face by a plane mirror. The eye to eye and ear to ear distances of her face are 4 inch and 6 inch respectively. The minimum widti. of the required mirror is :
(a) 1 inch
(b) 2 inch
(c) 3 inch
(d) 4 inch

Key Concepts

Symmetry in Reflection and Field of View

Because the mirror produces a symmetrical reflection, the observer’s field of view in the mirror is equally divided about the center of the object. This means that each eye sees one half of the object, and the mirror width needed to capture the entire object from one side to the other is only half the total width. This insight is key to solving problems involving the determination of minimal mirror dimensions for complete visibility.

Plane Mirror Reflection

This concept explains that a plane mirror forms a virtual image that appears to be located behind the mirror at the same distance as the object is in front. The angles of incidence and reflection are equal, resulting in a symmetric image. This symmetry allows one to determine which parts of an object are visible in the mirror based on the relative positions of the observer’s eyes and the mirror.

Minimum Mirror Size Requirement

The minimum mirror size needed for an observer to see an entire object is generally smaller than the object itself due to the reflective geometry. In particular, for viewing a full-dimension (like the width of a face), it turns out that only half of that dimension is necessary. This result arises from the fact that the light from the extreme points on the object reaches the observer's eyes via the mirror so that only a central portion of the mirror is used.

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