$A$ convex lens has a focal length $f$. It is cut into two parts along the dotted line as shown in the figure. The focal length of each part will be

$A$ convex lens has power $P$. It is cut into two halves along its principal axis. Further,one piece (out of two halves) is cut into two halves perpendicular to the principal axis as shown in the figure. Choose the incorrect option for the reported lens pieces.

$A$ prism having a refractive index $1.414$ and a refracting angle $30^{\circ}$ has one of its refracting surfaces silvered. $A$ beam of light incident on the other refracting surface will retrace its path if the angle of incidence is: (in $^{\circ}$)

In an experiment,a convex lens of focal length $15 \, cm$ is placed coaxially on an optical bench in front of a convex mirror at a distance of $5 \, cm$ from it. It is found that an object and its image coincide if the object is placed at a distance of $20 \, cm$ from the lens. The focal length of the convex mirror is.......$cm$.

$A$ concave mirror of focal length $f_{1}$ is placed at a distance $d$ from a convex lens of focal length $f_{2}$. $A$ parallel beam of light coming from infinity parallel to the principal axis falls on the convex lens and then after refraction falls on the concave mirror. If the light is to retrace its path,the distance $d$ should be:

$A$ biconvex lens of focal length $15 \,cm$ is in front of a plane mirror. The distance between the lens and the mirror is $10 \,cm$. $A$ small object is kept at a distance of $30 \,cm$ from the lens. The final image is