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.