A man of height 180 cm standing in front of plane mirror
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The mirror must be at least half as tall as the person standing in front of it. Since the person is 180 cm tall, the vertical dimension of the mirror must be at least 90 cm. The lower edge of the mirror must be at a height that is half the distance between his feet and eyes. Since the eyes are located 6 cm from the top of his head which means it is at a height of 174 cm from his feet, the lower edge of the mirror must be 87 cm from the ground.
Explanation : Understanding the solution requires an intermediate result using the law-of-reflection. When a ray of light is incident on a plane reflecting surface, the incident ray and the reflected ray will lie on the same plane. One can define the angles of incidence and reflection as follows:
Angle of incidence ≡ Angle between the incident ray and the normal to the reflecting surface at the point of incidence.
Angle of reflection ≡ Angle between the reflected ray and the normal to the reflecting surface at the point of incidence.
The law of reflection states that the angle of reflection is the same as the angle of incidence.
A Useful Result : Consider a situation where a light ray from an object gets reflected by a mirror and enters an eye, as illustrated in the figure below. If the object and the eye are at the same distance from the mirror then the law of reflection implies that the point of incidence lie exactly midway between the object and the eye.
Explanation : Understanding the solution requires an intermediate result using the law-of-reflection. When a ray of light is incident on a plane reflecting surface, the incident ray and the reflected ray will lie on the same plane. One can define the angles of incidence and reflection as follows:
Angle of incidence ≡ Angle between the incident ray and the normal to the reflecting surface at the point of incidence.
Angle of reflection ≡ Angle between the reflected ray and the normal to the reflecting surface at the point of incidence.
The law of reflection states that the angle of reflection is the same as the angle of incidence.
A Useful Result : Consider a situation where a light ray from an object gets reflected by a mirror and enters an eye, as illustrated in the figure below. If the object and the eye are at the same distance from the mirror then the law of reflection implies that the point of incidence lie exactly midway between the object and the eye.
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