The image of an object, formed by a plano-convex lens at distance of 8 m behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is \frac{2}{3} times the wavelength in free space. The radius of the curved surface of the lens is

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Question

The image of an object, formed by a plano-convex lens at distance of 8 m behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is $\frac{2}{3}$ times the wavelength in free space. The radius of the curved surface of the lens is

2 m

3 m

1 m

6 m

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$M = \frac{- x_{2}}{f}$

$\Rightarrow \frac{- 1}{3} = \frac{- 8}{f} ∴ f = 24 cm$

$\frac{1}{f} - (μ - 1) \frac{1}{R}$

$\frac{1}{24} = (\frac{3}{2} - 1) \frac{1}{R} ∴ R = 12 cm$

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