Let f1 be the focal length of convex lens; radius of curvature of each curved face is R.
1f1=(m−1){1R−(1−R)}=(μ−1)2R
⇒f1=R2(μ−1)=R2(32−1)=R
When the space between the lens and mirror is filled by water of refractive index μ1=4/3, then the focal length of liquid concave lens f2 is
1f2=(μ1−1)(−1R−∞)
⇒f2=−Rμ1−1=−R(43−1)=−3R
The combined focal length of lenses is F1=15cm
∴1F1=1f1+1f2⇒115=1R−13R=3−13R
⇒3R=30⇒R=10cm
In the second case,
F2=25cm. Let μ1=μ2
∴1F2=1f1+1f2⇒125=110+1f′2
⇒1f′2=125−110=2−550
∴f′2=−503cm
f′2=Rμ2−1⇒μ2−1=−Rf′2=−10(−50/3)=35=0.6
⇒μ2=1+0.6=1.6