The image of an object placed in air formed by a convex refracting surface is at a distance of 10 m behind the surface. The image is real and is at 2rd3 of the distance of the object from the surface. The wavelength of light inside the surface is 23 times the wavelength in air. The radius of the curved surface is x13 m . the value of ‘X’ is________

λm=λaμ⇒μ=32 μv−1u=μ−1R 32×10+115=32−1R R=3013 x=30

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The image of an object placed in air formed by a convex refracting surface is at a distance of 10 m behind the surface. The image is real and is at $\frac{2^{rd}}{3}$ of the distance of the object from the surface. The wavelength of light inside the surface is $\frac{2}{3}$ times the wavelength in air. The radius of the curved surface is $\frac{x}{13} m$ . the value of ‘X’ is________

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answer is 30.

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Detailed Solution

$λ_{m} = \frac{λ_{a}}{μ} \Rightarrow μ = \frac{3}{2} \frac{μ}{v} - \frac{1}{u} = \frac{μ - 1}{R} \frac{3}{2 \times 10} + \frac{1}{15} = \frac{\frac{3}{2} - 1}{R} R = \frac{30}{13} x = 30$

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