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Diameter of a plano - convex lens is 6 cm and its thickness at the centre is 3 mm. Then the focal length of the lens, if the speed of light in the material of lens is 2 × 10⁸ m/s

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45 cm

15 cm

7.5 cm

30 cm

answer is D.

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Detailed Solution

$μ = \frac{c}{v}, μ = \frac{3 \times 10^{8}}{2 \times 10^{8}} = 1.5 For plano covex lens$

$\frac{1}{f} = \frac{(μ - 1)}{R}, f = \frac{R}{(μ - 1)}; R^{2} = r^{2} + (R - y)^{2}$

$(∴ Neglecting y^{2})$

$R = \frac{r^{2}}{2 y} \Rightarrow R = \frac{9 \times 10^{- 4}}{2 \times 3 \times 10^{- 3}} = 0.15 m; R = 15 cm$

$Focal length f = \frac{15}{(1.5 - 1)} = 30 cm$

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