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 $$23rd$$ 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 $$x13m$$. The value of 'x' is $$______$$

Question

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  $$23rd$$ 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  $$x13m$$. The value of 'x' is $$______$$

Infinity Learn · Accepted Answer

λ$$m=$$λairμ⇒μ$$=32$$ Applying μ$$2v$$−μ$$1u=$$μ$$2$$−μ$$1R$$⇒μv−$$1u=$$μ−$$1RGiven$$ : $$v=+10$$ and $$u=-32v$$ $$=-15$$⇒$$320+115=1.5$$−$$1R$$⇒$$R=3013=x13$$∴$$x=30$$

Spherical refracting surface's

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Spherical refracting surface's

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λm=λairμ⇒μ=32 Applying μ2v−μ1u=μ2−μ1R⇒μv−1u=μ−1RGiven : v=+10 and u=-32v =-15⇒320+115=1.5−1R⇒R=3013=x13∴x=30

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