If a 2 m tall man is looking at a plane mirror from an eye which is 20 cm from the top of his 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?

I'm confused about where the source/destination of each light ray should be and how to find the distance and height of the mirror after I have drawn those rays.

Draw the light rays going backwards, starting from his eye. For a ray diagram, represent the object and mirror as two parallel vertical lines. Use any distance X apart; it won't affect the answer. One limiting light ray should go from his eye to the mirror, bounce off and hit the top of his head. The other limiting ray should go downward from his eye and bounce off to hit his shoes. There will be a virtual source on the opposite side of the mirror, an equal distance X away.

The only place you will actually need a mirror is between the two places where the limiting rays strike the mirror. The distance between them, using geometry, will turn out to be 1 meter. The bottom of the minimum-length mirror should be (2.0-0.2)/2 = 0.9 m above the ground.

The ans will be 0.9m

The answer depends on the man's FOV. Everyone sees differently. One person may be able to see everything within 165° while someone else may only be able to see 103°.

To determine the minimum length of the mirror and its height placement, we will need to use the concept of ray diagrams and the properties of reflection. Let's break down the problem step by step:

1. Start by drawing a diagram: Draw a vertical line to represent the man's height (2 meters). Draw a horizontal line perpendicular to the height line to represent the ground. The man's eye is located 20 cm from the top of his head, so mark a point on the height line for the eye. This forms a right-angled triangle with the ground, where the height of the triangle is 2 meters minus 20 cm.

2. Identify the ray paths: Now, imagine that light travels from the lowest point of the man's feet towards the mirror. Draw a ray from the man's foot at an angle such that it is reflected straight back towards his eye. This ray represents the bottommost point of the man's body that he should be able to see in the mirror.

3. Draw the reflected ray: Draw a reflected ray from the mirror such that it follows the law of reflection. According to the reflection law, the angle of incidence (angle between the incident ray and the mirror) is equal to the angle of reflection.

4. Intersection with the eye: Extend the reflected ray until it intersects with the line representing the man's eye. Now, draw the path of the light from the highest point of the man's head towards the mirror. This ray should also be reflected back towards his eye.

5. Find the intersection: Extend the second reflected ray until it intersects with the line representing the eye. The point of intersection of both reflected rays on the line of the eye represents the topmost point of the man's body that he can see in the mirror.

6. Measure the mirror length and its height placement: Measure the distance between the bottommost and topmost visible points on the eye line. This will give you the minimum length of the mirror required. Measure the height from the ground up to the eye line intersection point with the reflected rays. This will give you the height at which the mirror needs to be placed.

By following these steps, you should be able to determine the minimum length of the mirror and its height placement in order for the man to see his whole body.