A paperweight in the form of a hemisphere of radius $3.0 \mathrm{cm}$ is used to hold down a printed page. The paperweight is inverted at its place so that the spherical surface touches the paper. An observer looks at the page vertically through the paperweight. At what height above the page will the printed letters near the centre appear to the observer?

The radii of curvature of a lens are $+20 \mathrm{cm}$and $+30 \mathrm{cm}.$The material of the lens has a refracting index $1.6$. Find the focal length of the lens

(a) if it is placed in air and
(b) if it is placed in water $(\mathrm{\mu }=1.33)$.

A thin lens, made of a material of refractive index ${\mu }_2$ has a medium of refractive index ${\mu }_1$ on one side and a medium of refractive index ${\mu }_3$ on the other side. The lens is biconvex and the two radii of curvature have equal magnitudes, $R$. A beam of light travelling parallel to the principal axis is incident on the lens. Where will the image be formed, if the beam is incident from

(a) the medium ${\mu }_1$and

(b) from the medium ${\mu }_3$?

A convex lens has a focal length of $10 \mathrm{cm}$. Find the location and nature of the image if a point object is placed on the principal axis at a distance of

(a) $9.8 \mathrm{cm}$,

(b) $10.2 \mathrm{cm}$ from the lens.