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......$cm$.

The dotted part of the lens is cut and kept on the $x$-axis as shown in the diagram. If parallel paraxial rays are falling on this system,then the coordinate of the image formed after refraction from both the lenses is $(30, -1)$. If $x = 2.5 \, cm$,then $y = .......... \, cm$. (Assume the lens has no spherical aberration)

The distance between an object and the screen is $100 \ cm$. $A$ lens produces an image on the screen when placed at either of the positions $40 \ cm$ apart. The power of the lens is

$A$ converging beam of rays is incident on a diverging lens. Having passed through the lens,the rays intersect at a point $15\, cm$ from the lens on the opposite side. If the lens is removed,the point where the rays meet will move $5\, cm$ closer to the lens. The focal length of the lens is $......\, cm$.

The refractive index of the material of a double convex lens is $1.5$ and its focal length is $5 \,cm$. If the radii of curvature are equal, the value of the radius of curvature (in $cm$) is

$A$ turnip sits before a thin converging lens,outside the focal point of the lens. The lens is filled with a transparent gel so that it is flexible; by squeezing its ends toward its center [as indicated in figure $(a)$],you can change the curvature of its front and rear sides. When you squeeze the lens,the image: