The diagram shows a silvered equiconvex lens. An object of length 1 cm has been placed in the front of the lens. What will be the final image properties? The refractive index of the lens is μ and the refractive index of the medium in which the lens has been placed is 2μ. Both the surface have the radius R.

Engineering

Physics

Curved Surface Refraction

Lens

Question

The diagram shows a silvered equiconvex lens. An object of length 1 cm has been placed in the front of the lens. What will be the final image properties? The refractive index of the lens is μ and the refractive index of the medium in which the lens has been placed is 2μ. Both the surface have the radius R.

same size, erect and virtual

none

Half size, erect and virtual

same size, erect and real

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Applying
$\frac{1}{f_{l}} = (\frac{μ_{0}}{μ_{s}} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{L}})$
$\frac{1}{f_{l}} = (\frac{μ}{2 μ} - 1) (\frac{1}{R} - \frac{1}{- R}) = \frac{- 1}{2} \frac{2}{R} = - \frac{1}{R}$
$\frac{1}{f_{eq}} {(P_{ev})}_{M} = P_{M} + 2 P_{L}$
${(P_{eV})}_{M} = - (\frac{1}{- R / 2}) + 2 (\frac{- 1}{R}) = 0$
⇒ Behave as plane mirror.

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