A convex spherical refracting surface of refractive index $1.5$ forms the image of an object distant $10 \mathrm{cm}$ from it at a distance of $40 \mathrm{cm}$ on the same side as the object. What is the radius of curvature of the surface?

An empty spherical flask of diameter $100 \mathrm{cm}$ is placed in water $(n=\raisebox{1ex}{${\displaystyle 4}$}\!\left/ \!\raisebox{-1ex}{$3$}\right.)$. A parallel beam of light strikes the flask. Where will it appear to come from to an observer within the flask?

A point-object is placed in air at $40 \mathrm{cm}$ from a concave spherical surface of radius of curvature $20 \mathrm{cm}$ and refractive index $1.5$. Locate the image.

A point-object is $2.0 \mathrm{cm}$ below the concave meniscus of water $(n=\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.)$ of radius of curvature $0.5 \mathrm{cm}$. Locate the image.

A glass sphere of radius $5 \mathrm{cm}$ has a small bubble $2 \mathrm{cm}$ from its centre. The bubble is viewed along a diameter of the sphere, from the side on which it lies. How far from the surface will it appear? Refractive index of glass is $1.5$.

An air bubble is seen inside a solid sphere of glass $(n = 1.5)$ of $4.0 \mathrm{cm}$ Diameter at a distance of $1.0 \mathrm{cm}$ From the surface of the sphere (on seeing along the diameter). Determine the real position of the bubble inside the sphere.

One end of a cylindrical rod of glass $(n = 1.5)$ shown in the figure is given a spherical shape of the radius

$2.0 \mathrm{cm}$. On the left side of this end is placed an object $O$ at a distance of $12 \mathrm{cm}$. Find out the distance ($v$) of the image.

The radii of curvature of a double convex lens are $15 \mathrm{cm}$ and $30 \mathrm{cm}$ and the refractive index of its glass is $1.5$. Calculate the focal length of the lens.

The radii of curvature of a double concave lens are $30 \mathrm{cm}$ and $60 \mathrm{cm}$ and the refractive index of its glass is $1.5$. Calculate the focal length of the lens.