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:

$A$ 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.......$cm$

$A$ denser medium of refractive index $1.5$ has a concave surface of radius of curvature $12 \, cm$. An object is situated in the denser medium at a distance of $9 \, cm$ from the pole. Locate the image due to refraction in air.

$A$ point object is placed at the centre 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.....$cm$

$A$ curved surface of radius $R$ separates two media of refractive indices $\mu_1$ and $\mu_2$ as shown in figures $A$ and $B$. Choose the correct statement$(s)$ related to the virtual image formed by object $O$ placed at a distance $x$,as shown in figure $A$.

Three glass cylinders of equal height $H = 30 \text{ cm}$ and same refractive index $n = 1.5$ are placed on a horizontal surface as shown in the figure. Cylinder $I$ has a flat top,cylinder $II$ has a convex top,and cylinder $III$ has a concave top. The radii of curvature of the two curved tops are same $(R = 3 \text{ m})$. If $H_1, H_2$ and $H_3$ are the apparent depths of a point $X$ on the bottom of the three cylinders,respectively,the correct statement$(s)$ is/are:
$(1) H_3 > H_1$
$(2) 0.8 \text{ cm} < (H_2 - H_1) < 0.9 \text{ cm}$
$(3) H_2 > H_3$
$(4) H_2 > H_1$