$A$ 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 $\,cm$)

$A$ 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.....$cm$

Two transparent media having refractive indices $1.0$ and $1.5$ are separated by a spherical refracting surface of radius of curvature $30\,cm$. The centre of curvature of the surface is towards the denser medium and a point object is placed on the principal axis in the rarer medium at a distance of $15\,cm$ from the pole of the surface. The distance of the image from the pole of the surface is .......$cm$.

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?

$A$ spherical surface of radius of curvature $R$ separates air from glass of refractive index $1.5$. The centre of curvature is in the glass. $A$ point object $P$ placed in air forms a real image $Q$ in the glass. The line $PQ$ cuts the surface at point $O$ and $PO = OQ = x$. Hence the distance $x$ is equal to (in $R$)

$A$ point source of light at the surface of a sphere causes a parallel beam of light to emerge from the opposite surface of the sphere. The refractive index of the material of the sphere is