Challenges in optics 3

A thin biconvex lens of refractive index \(\frac{3}{2}\) is placed on a horizontal plane mirror. The space between the lens and the mirror is filled with water of refractive index \(\frac{4}{3}\). It is found that when a point object is placed 15cm above the lens on its principle axis, the object coincides with its own image. On repeating the same with another liquid, the object and image coincide at a distance 25cm from lens. Calculate the refractive index of the liquid.

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