Answer to Question #179735 in Physics for Jerick

Question

1.What is the focal length of a plane mirror? What is the magnification of a plane mirror?

2.Although a plane mirror appears to reverse left and right, it doesn’t reverse up and down. Discuss why this happens, noting that front to back is also reversed. Also discuss what happens if, while standing, you look up vertically at a horizontal mirror on the ceiling.

3.An object is placed along the principal axis of a spherical mirror. The magnification of the object is -2.0.  Is the image real or virtual, inverted or upright? Is the mirror concave or convex?  On which side of the mirror is the image located?

4.A person whose eyes are 1.72 m above the floor stands 2.20 m in front of a vertical plane mirror whose bottom edge is 38 cm above the floor as in figure below. What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror?

Answer 1

1. The focal length of a plane mirror is infinity. The magnification of a plane mirror is 1.
2. A plane mirror produces an image where points on the object closer to the mirror are have the same distance to the back surface of the mirror. So, when we stand on a horizontal image, the image is reversed upside down.
3. Only concave mirror can produce negative magnification, so, the image is real and inverted. The image is on the same side as the object.
4. Tangent of angle of incidence is equal to the angle of reflection:

$$\tan\theta=\frac{H-38}{220}=0.609,\\\space\\ x=\frac{38}{\tan\theta}=62.4\text{ cm}.$$