Index of Refraction of a lens+mirror

[Erubus]

Homework Statement

The radius of curvature of both sides of a converging lens is 18 cm. One side of the lens is coated with silver so that the inner surface is reflective. When light is incident on the uncoated side it passes through the lens, reflects off the silver coating, and passes back through the lens. The overall effect is that of a mirror with focal length 5.0 cm. What is the index of refraction of the lens material? (Answer 1.4)

Homework Equations

$\frac{1}{f}$=(n-1)($\frac{1}{R1}$-$\frac{1}{R2}$)

The Attempt at a Solution

I plugging in 5cm for f and 18cm for R1. For R2 I thought that because the mirror half of the lens has a focal length of 5cm, that the radius of the the silver coated side would be 10cm. I plug this into R2 however, this is incorrect probably because I'm not clear how the radius of curvature could change for either side, when it is stated at the beginning that both sides are 18cm.

 

[Simon Bridge]

because the mirror half of the lens has a focal length of 5cm, that the radius of the the silver coated side would be 10cm

You appear to have misread the question - the focal length of lens + mirror is 5cm.
The focal length for the mirror side by itself is not 5cm.

 

[Erubus]

Got it, thanks.