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  4. A boy is 1.8 m tall and can see his image in a plane mirror fixed on a wall. His eyes are 1.6 m from the floor level. The minimum length of the mirror is

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Q. A boy is 1.8 m tall and can see his image in a plane mirror fixed on a wall. His eyes are 1.6 m from the floor level. The minimum length of the mirror is

Ray Optics and Optical Instruments

Solution:

As the ray from feet enters the eye after striking the mirror at $M_{2}$, so height of $M_{2}$ from ground level is half of the eye level from ground, i.e., $\frac{1.6}{2}=0.8 \,m$.
image
Similarly, a ray from the head enters the eye after striking the mirror at $M_{1}$, so position of $M_{1}$ from the head level is half the distance between head and eye level.
i.e., $\frac{1.8-1.6}{2}=\frac{0.2}{2}=0.1 \,m$
So, minimum length of mirror is $[1.8-(0.8+0.1)]=0.9 m$ Minimum length of mirror is independent of the eye level because it is equal to the half the height of the boy.