A plano-convex lens, when silvered at its plane surface is equivalent to a concave mirror of focal length 28cm.when its curved surface is silvered and the plane surface not silvered,it is equivalent to a concave mirror of focal length 10cm,then the refractive index of the material of the lens is
Answers
Given:
A plano-convex lens, when silvered at its plane surface is equivalent to a concave mirror of focal length 28cm.
To find:
The refractive index of the material of the lens is
Solution:
Let fm be the focal length of the silvered surface.
A plano-convex lens, when silvered at its plane surface is equivalent to a concave mirror of focal length 28cm.
∴ fm = ∞
Thus, 1/28 = 2/f1 + 1/fm
1/28 =2/f1 + 0
∴ f1 = 56 cm
When it is equivalent to a concave mirror of focal length 10cm,
1/10 = 2/f1 + 1/fm
1/10 = 1/56 + 1/fm
solving for fm, we get,
∴ fm = 140/9 cm
The radius of curvature,
R = 2fm
R = 2 × 140/9
∴ R = 280/9 cm
The refractive index is given by,
1/f1 = (μ - 1) 1/R
1/56 = (μ - 1) × 9/280
280 / (9 × 56) + 1 = μ
∴ μ = 14/9
Therefore, the refractive index of the material of the lens is 1.555