$A$ point object $O$ is placed in front of a glass rod having a spherical end of radius of curvature $30\; cm$ as shown in the figure. The image would be formed at:

As shown in the figure,region $BCDEF$ and $ABFG$ have refractive indices $2.0$ and $1.5$ respectively. $A$ particle $O$ is kept at the midpoint of region $BCEF$. The final image of the object as seen by the eye is at a distance of:

An air bubble in a glass sphere having a $4 \,cm$ diameter appears $1 \,cm$ from the surface nearest to the eye when looked at along the diameter. If the refractive index of glass is $_a\mu_g = 1.5$,the actual distance of the bubble from the refracting surface is.....$cm$.

$A$ clear transparent glass sphere $(\mu=1.5)$ of radius $R$ is immersed in a liquid of refractive index $1.25$. $A$ parallel beam of light incident on it will converge to a point. The distance of this point from the center will be

$A$ point object $O$ is placed on the axis of a cylindrical piece of glass of refractive index $1.6$ as shown in the figure. One surface of the glass piece is convex with a radius of curvature $3 \,mm$. The point appears to be at $5 \,mm$ on the axis when viewed along the axis from the right side of the convex surface. The distance of the point object from the convex surface is: (in $\,mm$)

$A$ point object $O$ is placed in front of a glass rod having a spherical end of radius of curvature $30 \,cm$. The image would be formed at