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JEE Main 2015 · 10 Apr · Shift 1, Physics question 26

A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm. If a 50 m tall tower at a distance of 1 km is observed through this telescope in normal setting, the angle formed by the image of the tower is θ, then θ is close to :

Choose one option
Answer and worked solution

Official answer: D

The tower subtends tan⁡α=501000=0.05\tan\alpha=\frac{50}{1000}=0.05 at the objective. In normal adjustment the angular magnification is 1505=30\frac{150}5=30, so the image subtends tan⁡θ=30×0.05=1.5\tan\theta=30\times0.05=1.5, i.e. θ≈56∘\theta\approx56^\circ. The closest option is 60°.

Topics:Optical instruments
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