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Question
A double convex lens has two surfaces of equal radii R and refractive index \[m = 1 \cdot 5\]
Options
\[f = R/2\]
- \[f = R\]
\[f = - R\]
\[f = 2R\]
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Solution
f = R
As from lens maker formula:
\[\frac{1}{f} = (m - 1)(\frac{1}{R_1} - \frac{1}{R_2})\]
\[ \Rightarrow \frac{1}{f} = (1 . 5 - 1)(\frac{1}{R} - \frac{1}{- R}) (\text{ As given } R_1 = R_2 = R)\]
\[ \frac{1}{f} = (0 . 5)(\frac{1}{R} + \frac{1}{R})\]
\[ \frac{1}{f} = (0 . 5)(\frac{2}{R})\]
\[ f = R\]
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