If in a plano-convex lens,the radius of curvature of the convex surface is $10 \ cm$ and the focal length of the lens is $30 \ cm,$ then the refractive index of the material of the lens will be

The radii of curvature of the faces of a double convex lens are $10\,cm$ and $15\,cm$. Its focal length is $12\,cm$. What is the refractive index of glass?

$A$ particle executes linear $S.H.M.$ along the principal axis of a convex lens of focal length $8 \,cm$. The mean position of oscillation is at $14 \,cm$ from the lens with amplitude $1 \,cm$. The amplitude of the oscillating image of the particle is nearly: (in $\,cm$)

$f_v$ and $f_r$ are the focal lengths of a convex lens for violet and red lights respectively,and $F_v$ and $F_r$ are the magnitudes of the focal lengths of a concave lens for violet and red lights respectively. Then:

$A$ photograph of a landscape is captured by a drone camera at a height of $18 \ \text{km}$. The size of the camera film is $2 \ \text{cm} \times 2 \ \text{cm}$ and the area of the landscape photographed is $400 \ \text{km}^2$. The focal length of the lens in the drone camera is: (in $\text{cm}$)

$A$ lens forms real and virtual images of an object when the object is at $u_1$ and $u_2$ distances respectively. If the size of the virtual image is double that of the real image,then the focal length of the lens is (Take the magnification of the real image as $m$)