Exercise 5: A plane mirror is hanging on a vertical wall; a boy \( 1.6 \mathrm{~m} \) tall wants to see both his feet and top of his head in the mirror when he is standing erect.
Assuming his eyes are \( 15 \mathrm{~cm} \) below the top of his head find
(i) The minimum height of the mirror.
(ii) Its distance from the floor.
Answer
\( \mathrm{Distance~from~the~floor} = 1.1625 \mathrm{~m} \)
Step 1 ：\( \mathrm{Let~the~minimum~height~of~the~mirror} = h \)
Step 2 ：\( \mathrm{It~forms~1:1~ratio~of~the~image~because~mirror~distance~=~object~distance} \)
Step 3 ：\( h = \frac{1.6 - 0.15}{2} \)
Step 4 ：\( h = 0.725 \mathrm{~m} \)
Step 5 ：\( \mathrm{Distance~from~the~floor} = \frac{1.6 + 0.725}{2} \)
Step 6 ：\( \mathrm{Distance~from~the~floor} = 1.1625 \mathrm{~m} \)
