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 times the wavelength in free space. The radius of the curved surface of the lens is

Engineering

Physics

Curved Surface Refraction

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

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

$\frac{1}{f} - (μ - 1) \frac{1}{R}$

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