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  • A person has been using spectacles of power −1.0 dioptre for distant vision and a separate reading glass of power 2.0 dioptres. What is the least distance of distinct vision for this person :

A person has been using spectacles of power −1.0 dioptre for distant vision and a separate reading glass of power 2.0 dioptres. What is the least distance of distinct vision for this person :

Option: 1

40 cm


Option: 2

30 cm


Option: 3

10 cm


Option: 4

50 cm


Answers (1)

best_answer

Power convex lens = 2.0 D
Power of concave lens = –1.0 D

x\rightarrow least distance of distinct vision

\begin{aligned} & \mathrm{f}=\frac{1}{2} \times 100=50 \mathrm{~cm} \\ & \frac{1}{\mathrm{f}}=\frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}} \\ & \frac{1}{50}=\frac{1}{(-\mathrm{x})}-\frac{1}{-25} \Rightarrow \frac{1}{50}-\frac{1}{25}=\frac{1}{(-\mathrm{x})} \\ & \Rightarrow \quad \frac{1-2}{50}=\frac{-1}{\mathrm{x}} \\ & \Rightarrow \quad x=50 \mathrm{~cm} \end{aligned}

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