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

$A$ convex refracting surface of radius of curvature $20 \, cm$ separates two media of refractive indices $\frac{4}{3}$ and $1.6$. An object is placed in the first medium $(\mu = 4/3)$ at a distance of $200 \, cm$ from the refracting surface. The position of the image formed is.....$cm$

Light from a point source in air falls on a spherical glass surface (refractive index,$\mu=1.5$ and radius of curvature $=50\ cm$). The image is formed at a distance of $200\ cm$ from the glass surface inside the glass. The magnitude of distance of the light source from the glass surface is . . . . . . $m$.

$A$ small object is placed in the air, at a distance of $45 \,cm$ from a convex refracting surface of radius of curvature $15 \,cm$. If the surface separates air from glass of refractive index $1.5$, then the position of the image is: (in $\,cm$)

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

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: