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

$A$ diminished image of an object is to be obtained on a screen $1.0 \ m$ from it. This can be achieved by appropriately placing

Given below are two statements:
Statement $(I)$: When an object is placed at the centre of curvature of a concave lens,the image is formed at the centre of curvature of the lens on the other side.
Statement $(II)$: $A$ concave lens always forms a virtual and erect image.
In the light of the above statements,choose the correct answer from the options given below:

When the object is at distances $u_1$ and $u_2$ from a lens,the images formed are real and virtual respectively,and both have the same size. Then the focal length of the lens is:

$A$ lens is made of glass having an index of refraction $1.5$. One side of the lens is flat and the other side is convex with a radius $R$. If an object is placed $60 \ cm$ towards the convex side of the lens, the image is formed at $120 \ cm$ on the other side of the lens. The value of $R$ is (in $cm$)

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 $\frac{20}{3} \ cm$?