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Question

An object of height \( 3 \, \text{cm} \) is placed \( 20 \, \text{cm} \) from a concave mirror of focal
length \( 15 \, \text{cm} \). What is the height of the image?

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Explanation

**Microscope principle** objective of short focal length forms real image between F_e and 2F_e of eyepiece, eyepiece magnifies to virtual image at D, total magnification product, for f_o=2 cm, f_e=5 cm, L=20 cm, m_o≈10, M_e≈6, M≈60, illustrating high magnification from two stages. f = -15 cm , u = -20 cm . (1/v) + (1/-20) = (1/-15) ⇒ (1/v) = (1/-15) + (1/20) = (-4 + 3/60) = (-1/60) . v = -60 cm . Magnification: m = -(v/u) = -(-60/-20) = -3 . Image height: h' = m × h = -3 × 3 = -9 cm (inverted). Magnitude = 9 cm . Substituting

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