Physics 2.3 Waves

[NickC]

Hi,

I was just wondering about two questions I was trying to do in an ESA study guide.

Activity 5A: Plane mirrors

1. A ray of light makes an angle on 25 degrees with the normal to a plane mirror. The mirror is turned 6 degrees so that the answer becomes 31 degrees. Through what angle is the reflected ray rotated?

2. A boy 1.5 m tall whose eyes are 1.4m from the floor when he stands straight, can just see his complete image in a wall mirror.

a) What is the smallest length, l, of the mirror that allows the boy to see his complete image? The mirror is on a wall 3.0m from the boy.

2b) What is the height, h, of the mirror’s bottom edge from the floor?

The answer to 1) is 12 degrees, the answer to 2a) is 0.75m and the answer to 2b) is 0.70m. I don’t know how to work out these answers.

Can anyone help me?

[scienceteacher]

1. The reflected ray will also be 31 degrees (from the new position of the normal). As the mirror has been rotated by 6 degrees, the normal has been rotated by 6 degrees also. So the total rotation of the reflected ray will be 12 degrees (6 due to the increase in the incident angle, and 6 from the rotation of the normal).
2. The rays from any part of his body to the mirror will be reflected at equal angles. Therefore the point at which they are incident on the mirror will be halfway between their origin and his eye. So the ray from the bottom of his foot that goes back to his eye will be incident on the mirror at 1.4/2=0.70m above the floor.
   The ray from the top of his head that goes back to his eye will be incident on the mirror 0.05m below the top of his head. So the minimum height of the mirror is 1.5-(0.70+0.05)=0.75m. Note that while the distance of the boy from the mirror will affect the angle, it won’t affect the required height or position of the mirror.