Question 321: Ray Optics

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 $${{{2^{rd}}} \over 3}$$ of the distance of the object from the surface. The wavelength of light inside the surface is $${2 \over 3}$$ times the wavelength in air. The radius of the curved surface is $${x \over {13}}$$ m. The value of 'x' is ___________.

Accepted Answer

$${{{\mu _2}} \over v} - {{{\mu _1}} \over u} = {{{\mu _2} - {\mu _1}} \over R}$$
$${\mu _1} = 1$$, $${\mu _2} = 1.5$$
$${{1.5} \over { + 10}} - {1 \over { - 15}} = {{1.5 - 1} \over { + R}}$$
$$R = {{30} \over {13}}$$ m

Ray Optics

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