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  • A hemispherical paper weight contains a small artificial flower of transverse size 2mm on its axis of symmetry at a distance of 4cm from its flat surface. What is the size of the flower as it appea

A hemispherical paper weight contains a small artificial flower of transverse size 2mm on its axis of symmetry at a distance of 4cm from its flat surface. What is the size of the flower as it appears to an observer when he looks at it along the axis of symmetry from the top? (Radius of the hemisphere is 10cm. Index of refraction of glass = 1.5).

Option: 1

1.5 mm


Option: 2

2 mm


Option: 3

2.5 mm


Option: 4

None of these


Answers (1)

best_answer

Here  \mathrm{m=\frac{h_i}{h_0}=\frac{\mu_1 \mathrm{v}}{\mu_2 u}}

From the question,
\mathrm{\mu_1=1.5, \mu_2=1 \\ }

\mathrm{ u=-6 \mathrm{~cm}, \quad \mathrm{v}=? }

\mathrm{\therefore \quad ~Using ~\frac{\mu_2}{\mathrm{v}}-\frac{\mu_1}{\mathrm{u}}=\frac{\mu_2-\mu_1}{\mathrm{R}} }  

we have

\mathrm{ \frac{1}{v}-\frac{1.5}{-6}=\frac{1-1.5}{-10} \quad \Rightarrow \quad v=-5 \mathrm{~cm} \\ }

\mathrm{ \therefore \quad \frac{h_i}{h_0}=\frac{h_i}{2 m m}=\frac{1.5 \times-5}{1 \times-6}=1.25 \\ }
\mathrm{ \Rightarrow h_i=2.5 \mathrm{~mm} }
 

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vinayak

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