Question

The convex surface of a thin concave-convex lens of glass of refractive index $1.5$ has a radius of curvature $20$cm. The concave surface has a radius of curvature $60$cm.

Answer 1

Now the given case can be considered as combination of
1. A thin lens of Radius of curvatures given by R1= infinity and R2= -60 cm
and μ = 1.33 refractive index of water
it is a thin lens
thus focal length of this lens is f1= 181.81 cm.
2. A concavo convexlength of  R1= -60 and R2= -20 cm
and  μ = 1.5
thus focal length of it for the case of thin lens is f2=60 cm
and
3.A concave mirror of focal length f3=\dfrac{-R}{2}=-10cm
3. A concave mirror of focal length f3= -R/2 = -10 cm
where R= 20cm
thus resultant focal length becomes 1/f = 1/f1 + 1/f2 + 1/f3
 as distances between the lenses are zero
thus resultant focal length is -12.85 cm.