$A$ glass concave lens is placed in a liquid in which it behaves like a convergent lens. If the refractive indices of glass and liquid with respect to air are $_a \mu_g$ and $_a \mu_l$ respectively,then

$A$ convex lens has its radii of curvature equal. The focal length of the lens is $f$. If it is divided vertically into two identical plano-convex lenses by cutting it,then the focal length of the plano-convex lens is ($\mu =$ the refractive index of the material of the lens).

If sunlight is focused on a paper using a convex lens,it starts burning the paper in the shortest time when the lens is kept at $30 \text{ cm}$ above the paper. If the radius of curvature of the lens is $60 \text{ cm}$,then the refractive index of the lens material is $\frac{\alpha}{10}$. The value of $\alpha$ is . . . . . . .

$A$ point source is located at a distance of $20 \ cm$ from the front surface of a symmetrical glass biconvex lens with equal radii of curvature $5 \ cm$. The distance at which the image is formed from the rear surface of this lens is $[$Given refractive index of the glass is $1.5]$

$A$ convex lens is made of $3$ layers of glass of $3$ different materials as shown in the figure. $A$ point object is placed on its axis. The number of images of the object formed is:

An object of height $25 \ cm$ is placed in front of a convex lens of focal length $30 \ cm$. If the height of the formed image is $50 \ cm$,then the distance between the object and the image is ..... $cm$.