When one surface of a biconvex lens is silvered then in this situation , Two times refraction through lens and one time reflection occurs
So power of combination
P = PL+Pm+PL = 2PL+Pm
Pm=-1fm , fm=R2 , PL = 1fL (fL is in metre )
for plano convex lens
two cases may arise
CASE-I
If plane surface is silvered
let radius of curvature is R and μ be its refractive index
P = 2PL + Pm
PL = 1fL = (μ-1)\left[\frac{1}{R}-\frac{1}{-\infty } \right]
\Rightarrow P_{L} = \frac{(\mu -1)}{R}
PM = -1fm = -1∞ = 0
hence P = 2(μ-1)R , f = R2(μ-1)
CASE - II
if curved surface is silvered
P = 2PL+Pm
P_{L} = (\mu -1)\left[\frac{1}{\infty } -\frac{1}{-R}\right] = \frac{(\mu -1)}{R}
Pm = -1fm = -1-R/2 = 2R
hence P = 2μR and f = R2μ