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An object $2.4 \mathrm{~m}$ in front of a lens forms a sharp image on a film $12 \mathrm{~cm}$ behind the lens. A glass plate $1 \mathrm{~cm}$ thick, of refractive index $1.50$ is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object be shifted to be in sharp focus on film?
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The correct answer is:
$5.6 \mathrm{~m}$
$5.6 \mathrm{~m}$
Case $\mathrm{I}: \mathrm{u}=-240 \mathrm{~cm}, \mathrm{v}=12$, by Lens formula
$\frac{1}{f}=\frac{7}{80}$
Case $\mathrm{II}$: $\mathrm{v}=12-\frac{1}{3}=\frac{35}{3}$ (normal shift $=1-\frac{2}{3}=\frac{1}{3}$ )
$f=\frac{7}{80}$
$u=5.6$
$\frac{1}{f}=\frac{7}{80}$
Case $\mathrm{II}$: $\mathrm{v}=12-\frac{1}{3}=\frac{35}{3}$ (normal shift $=1-\frac{2}{3}=\frac{1}{3}$ )
$f=\frac{7}{80}$
$u=5.6$
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