Solving Refraction Puzzles: Coin Depth & Convex Lens Image

[zimrock]

Problem 1:
A thin hollow glass sphere has a radius of 1 m. A coin is placed at the bottom of the glass sphere. 2.09 metre cube of a liquid of refractive index 1.5 is poured into the glass shpere. A person is viewing the object vertically. What is the apparent depth of the coin?

Im not sure if there will be refraction at the glass surface and i don't know how to consider it. I need help.

Problem 2:
A convex lens has a thickness 0.2m. The radii of curvature of the two surfaces are 1 and 2 m respectively. An object is kept at a distance of 10m from the left surface. The right surface is silvered. Find the position of final image.

I considered refraction at surface 1 , refration at surface 2, then reflection and then again refraction at surface 2 and refration at surface 1.
Is that right?

 

[mgb_phys]

1, The glass is a 'thin shell' so ignore it's refraction. You just have to consider a plano-spherical lens of water of whatever thickness that depth works out as.

2, Nearly, there is no refraction at surface 2 because there is no other medium between the glass and the silver. ( Ignoring complicated stuff about evervescent waves and surface plasmons).

 

[zimrock]

My book says, when there is a silvered lens, we are supposed to consider it as a lens and a mirror separately and consider 4 refractions and 1 reflection. I am unable to verify this from any standard textbook. Any source you'll suggest?