Calculating Refraction at a Spherical Surface with Multiple Media

[zorro]

Homework Statement

The radius of curvature of spherical surface is 10 cm. The spherical surface separates two media of refractive indices 1.1 and 1.3 as shown in Figure. The medium of refractive index 1.3 extends upto 78 cm from the spherical surface. A luminous point object O is at the distance of 144 cm from the spherical surface in the medium of refractive index 1.1. The image formed by the spherical surface is at

1)900 cm from O
2)900 cm from A in medium μ₃
3)900/7 cm from O
4)900/7 cm from A in medium μ₃

The Attempt at a Solution

The first two mediums act as glass slabs of thickness 66cm and 78cm resp.
Shift produced due to them = 24cm
New distance of the object from the spherical surface = 144-24=120cm

Using the formula of refraction at a spherical surface,

1.5/v + 1/120 = 0.5/10 (I kept μ as 1, may be I am wrong here)

I got v=36cm from O which is not in the options.

 

[sachin123]

Hey.
I'm not sure about anything,
but I don't find the normal shift you consider alright.(you consider '1' as the reference refractive index which is nowhere)
According to me,you must make an observer stand near the refracting surface(in the medium 1.3) and
find the apparent position of the object from there.
or...
make an observer stand near the object(in the medium 1.1) and find the app position of the refracting surface.
I am confused which...

Am I right?sorry if not