$A$ 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 $f$)

Provide the object distance,image distance,type,size,and magnification for an object placed in front of a thin convex lens for different positions.

When a convex lens is immersed in a liquid of refractive index equal to $80 \%$ of the refractive index of the material of the lens,the focal length of the lens increases by $100 \%$. The refractive index of the liquid 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 $cm$)

For a convex lens,the distance of the object is taken on the $X$-axis and the distance of the image is taken on the $Y$-axis. The nature of the graph so obtained is:

The focal length of a convex lens is $10 \ cm$ and its refractive index is $1.5$. If the radius of curvature of one surface is $7.5 \ cm$,the radius of curvature of the second surface will be......$cm$.