A thin glass (refractive index 1.5) lens has optical power of -5 D in… | JEE Main 2005 (AIEEE)

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Spherical Surfaces & Thin Lenses

A thin glass (refractive index $1.5$ ) lens has optical power of $-5\ D$ in air. Its optical power in a liquid medium with refractive index $1.6$ will be

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Answer: (b)

Power in a medium of index $n$ : $P = \frac{n}{f}$ , with $\frac{1}{f} = \left(\frac{\mu}{n} - 1\right)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$ .
In air: $-5 = (1.5 - 1)K \Rightarrow K = \left(\frac{1}{R_1} - \frac{1}{R_2}\right) = -10\text{ m}^{-1}$
In liquid: $\frac{1}{f} = \left(\frac{1.5}{1.6} - 1\right)(-10) = 0.625\text{ m}^{-1}$
$P = 1.6 \times 0.625 = +1\text{ D}$
So the answer is (b) $1\ D$ .

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