In the given figure, a ray of light 1cm above the principal axis get reflected from a concave mirror and intersect the principal axis at Y. Find the length PY if the radius of curvature of the mirror is 2cm.
A
(√3−1)cm
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B
2(1−1√3)cm
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C
(1−1√3)cm
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D
√3cm
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Solution
The correct option is B2(1−1√3)cm
In △ABC, sinθ=BCAC ⇒sinθ=12[AC=R=2cm] ⇒θ=30∘
Now, focal length, PY=R−R2secθ ⇒PY=R−R2sec30∘ ⇒PY=2−22×2√3 ⇒PY=2(1−1√3)cm