Solution:
Using Lens Maker's formula for a plano-convex lens: \(\frac{1}{f} = (\mu - 1)\frac{1}{R} ⇒ \frac{1}{30} = (\mu - 1)\frac{1}{10} ⇒ \mu - 1 = \frac{1}{3} ⇒ \mu = \frac{4}{3}\).
The refractive index of material of a plano-convex lens, if the radius of curvature of convex surface is 10 cm and focal length of lens is 30 cm is
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