If a 1.75 m tall man is looking at a plane mirror from an eye which is 15 cm from the top of their head, what is the minimum length that the mirror must be so that he can just barely see his whole body in the mirror? How far up from the ground must the mirror be placed?

1/(object distance) + 1/(image distance) = 1/(focal length)

Magnification = image height/(object height) = -image distance/(object distance)

3 answers

.875 m

cbnbc

To find the minimum length that the mirror must be for the man to see his whole body, we need to use the mirror equation:

1/(object distance) + 1/(image distance) = 1/(focal length)

Let's assume the height of the man is h meters. The object distance (distance between the man and the mirror) is the distance from the man's eye to the top of his head (15 cm or 0.15 m) plus his height (1.75 m). So, the object distance is 1.75 m + 0.15 m = 1.90 m.

For the man to see his whole body, the image distance must be equal to the height of the man (h). Therefore, 1/(image distance) = 1/h.

Now, substituting the values into the mirror equation, we have:

1/(1.90) + 1/(h) = 1/(focal length)

Simplifying the equation, we get:

1/(h) = 1/(focal length) - 1/(1.90)

To find the minimum length that the mirror must be, we need the focal length of the mirror. In this case, we assume a regular plane mirror which has a focal length of infinity. So, 1/(focal length) = 0.

Now, the equation becomes:

1/(h) = 0 - 1/(1.90) = -1/(1.90)

Simplifying further, we get:

1/(h) = -1/(1.90)

Now, we can solve for h by taking the reciprocal of both sides:

h = -1.90

Since height cannot be negative, this means that there is no minimum length for the mirror to see the man's whole body. The mirror can be any length as long as the man can see his feet in the mirror.

To determine how far up from the ground the mirror must be placed, it depends on the height of the man. In this case, the mirror can be placed on the ground, and the man will be able to see his whole body in the mirror.