$A$ beam of diameter $d$ is incident on a glass hemisphere as shown. If the radius of curvature of the hemisphere is very large in comparison to $d$,then the diameter of the beam at the base of the hemisphere will be:

Locate the image formed by refraction in the situation shown in the figure.

An image is formed at a distance of $100 \ cm$ from the glass surface when light from a point source in air falls on a spherical glass surface with a refractive index of $1.5$. The distance of the light source from the glass surface is $100 \ cm$. The radius of curvature is (in $cm$)

$A$ luminous point object $O$ is placed at a distance $2R$ from the spherical boundary separating two transparent media of refractive indices $n_1$ and $n_2$ as shown,where $R$ is the radius of curvature of the spherical surface. If $n_1 = \frac{4}{3}$,$n_2 = \frac{3}{2}$ and $R = 10 \text{ cm}$,the image is obtained at a distance from $P$ equal to:

Write the equation for the image formed by a curved surface of radius of curvature $R$ in a medium of refractive index $n_1$.

An air bubble in a glass sphere $(\mu=1.5)$ is situated at a distance $3\; cm$ from a convex surface of diameter $10\; cm$. At what distance from the surface will the bubble appear (in $; cm$)?