Minimum Length Of Plane Mirror To See Full Image

 

Minimum Length Of Plane Mirror To See Full Image :- Let’s consider a boy of height H standing in front of a vertical plane mirror. The goal is to see the full image of the boy, from head to toe. For this to happen, rays from both the head and the feet must reflect off the mirror and reach the observer’s eyes.

Using simple ray diagrams and geometry, we find that :

• A ray from the feet reflects off the lower half of the mirror.
• A ray from the head reflects off the upper half of the mirror.
• The eye is generally located at some height y between the head and the feet.

From the ray diagram we see that :

minimum length of plane mirror to see full image of boy = (x/2) + (y/2)  =  (x+y)/2  =  H/2

Due to the symmetry of reflection, it turns out that each point on the body requires only half the distance to be reflected back to the eye.

Conclusion

To see our entire reflection in a plane mirror, we don’t need a mirror as tall as we are. Instead, we only need a mirror that is half of our height. This result elegantly illustrates the laws of reflection and the geometry of image formation, making it a perfect example of practical physics in action.