A man of height H = 3/2 m , wants to see himself in plane mirror from top to bottom. The plane mirror is inclined with vertical wall at angle α = 5 3 ∘ . If the least size of mirror to see him is x m,

Question

A man of height H = 3/2 m , wants to see himself in plane mirror from top to bottom. The plane mirror is inclined with vertical wall at angle α = 5 3 ∘ . If the least size of mirror to see him is x m, the perpendicular distance of eye from mirror is d = 3 m , find the value of x .

TestHub · Accepted Answer

With d h ​ = tan θ and triangle geometry: c o s θ c o s ( α + θ ) d ​ = s i n 2 θ H ​ . Simplifying: 2 d = H [ cos α cot θ − sin α ] = h H d c o s α ​ − H sin α . h = 2 d + H s i n α H d c o s α ​ = 2 × 3 + 2 3 ​ × 5 4 ​ 2 3 ​ × 3 × 5 3 ​ ​ = 36/5 27/10 ​ = 8 3 ​ = 0.375 m

Physics - Geometrical Optics Question with Solution | TestHub

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