The radius of curvature of a curved surface of a . . .

Question : The radius of curvature of a curved surface of a plano convex lens is 10 cm and the refractive index is 1.5. If the plane surface is silvered, then the focal length will be :

a) 15 cm

b) 20 cm

c) 5 cm

d) 10 cm

Doubt by Angad

Solution : 

µ₂₁=1.5

R₁=+10 cm
R₂ = ∞

Note : When the surface of a any lens is silvered then it will act like a mirror whose focal length is given by 

1/F = (1/F_l)+(1/F_m)+(1/F_l)
OR
1/F = (2/F_l)+(1/F_m)

where
F = Equivalent Focal Length
F_l=Focal Length of the Lense
F_m=Focal length of the Mirror

In our case 
Focal length of the Lens can be calculate by using Len's Maker's Formula 

1/F_l=(µ₂₁-1)[1/R₁+1/R₂]
1/F_l=(1.5-1)[1/10+1/∞]
1/F_l=0.5(1/10)
1/F_l=5/100
1/F_l=1/20
F_l=20 cm 

Now for Resultant Focal Length 
1/F = (2/F_l)+(1/F_m)
Where F_m=Focal Length of the Mirror =  ∞

1/F=(2/20)+(1/ ∞)
1/F=2/20

1/F=1/10
F=10 cm 

Hence, d) 10 cm would be the correct option.