Light from a point source in air falls on a spherical glass surface ($n = 1.5$ and radius of curvature $= 20\; cm$). The distance of the light source from the glass surface is $100\; cm$. At what position (in $cm$) the image is formed?

Two identical glass rods $S_1$ and $S_2$ (refractive index $= 1.5$) have one convex end of radius of curvature $10 \ cm$. They are placed with the curved surfaces at a distance $d$ as shown in the figure,with their axes (shown by the dashed line) aligned. When a point source of light $P$ is placed inside rod $S_1$ on its axis at a distance of $50 \ cm$ from the curved face,the light rays emanating from it are found to be parallel to the axis inside $S_2$. The distance $d$ is (in $cm$)

Consider a point object $O$ situated at a distance of $30 \ cm$ from the centre of a sphere of radius $2 \ cm$ and refractive index $\mu_2 = 1.5$ as shown in the figure. If the refractive index of the region surrounding this sphere is $\mu_1 = 1.4$, then the position of the image due to refraction by the sphere with respect to the centre is:

$A$ ray coming from an object which is situated at infinity in the air falls on a spherical glass surface $(n=1.5)$. The distance of the image will be . . . . . . . ($R$ is the radius of curvature of the spherical glass surface.)

Light from a point source in air falls on a convex curved surface of radius $20 \,cm$ and refractive index $1.5$. If the source is located at $100 \,cm$ from the convex surface,the image will be formed at what distance from the object?

The figure shows a transparent sphere of radius $R$ and refractive index $\mu$. An object $O$ is placed at a distance $x$ from the pole of the first surface so that a real image is formed at the pole of the exactly opposite surface. If an object is placed at a distance $R$ from the pole of the first surface,then the real image is formed at a distance $R$ from the pole of the second surface. The refractive index $\mu$ of the sphere is given by