In the figure shown,$O$ is the centre of the glass sphere. The spot $P$ on the sphere,when viewed almost normally,appears:

$A$ parallel beam of light travelling in water (refractive index $\mu_1 = 4/3$) is refracted by a spherical air bubble of radius $R = 2 \, cm$ situated in water. Assuming the light rays to be paraxial,the position of the image due to refraction at the first surface is:

$A$ point object is placed at the center of a glass sphere of radius $6 \ cm$ and refractive index $1.5$. The distance of the virtual image from the surface of the sphere is.......$cm$

$A$ parallel beam of light is allowed to fall on a transparent spherical globe of diameter $30 \,cm$ and refractive index $1.5$. The distance from the centre of the globe at which the beam of light can converge is . . . . . . $mm$.

$A$ spherical glass is attached to a rigid wall as shown in the figure. An observer located at point $O$ is looking at a point $A$ on the wall. The refractive index of the glass is $1.5$ and that of air is $1.0$. The distances are $OA = 8 \text{ cm}$, $XA = 3 \text{ cm}$. If the radius of curvature of the spherical glass surface is $R = 5 \text{ cm}$, then the apparent distance of $A$ from the observer $O$ is (in $\text{ cm}$)

Derive the relation between object distance $(u)$,image distance $(v)$,refractive indices of the media ($n_1$ and $n_2$),and the radius of curvature $(R)$ for a spherical refracting surface.