What is the refractive index of the material of a double convex lens having radii of curvature of $5 \ cm$ and $10 \ cm$ and focal length of $\frac{20}{3} \ cm$?

$A$ convex lens is dipped in a liquid whose refractive index is equal to the refractive index of the lens material. Then its focal length will

$A$ thin convex lens of focal length $f$ made of crown glass is immersed in a liquid of refractive index $\mu_l$ $(\mu_l > \mu_c)$, where $\mu_c$ is the refractive index of the crown glass. The convex lens now acts as:

$A$ convex lens $T$ is used to form an image whose size is one-fourth that of the size of the object. Then the object distance is (in $f$)

An object is placed at a distance of $4\,cm$ in front of a concave lens of focal length $12\,cm$. The nature and position of the image from the lens is

$A$ convex lens makes a real image $4 \, cm$ long on a screen. When the lens is shifted to a new position without disturbing the object,we again get a real image on the screen which is $16 \, cm$ tall. The length of the object must be.......$cm$