$A$ double convex lens made of glass has both radii of curvature of magnitude $20 \,cm$. Incident light rays parallel to the axis of the lens will converge to a point at a distance $L$ from the common pole $P$. The value of $L$ is [Refractive index of glass $= 1.5$].

When blue light is used instead of red light in a convex lens,its focal length will ......... .

$A$ plano-convex lens having a radius of curvature of the first surface $2 \ cm$ exhibits a focal length of $f_1$ in air. Another plano-convex lens with a first surface radius of curvature $3 \ cm$ has a focal length of $f_2$ when it is immersed in a liquid of refractive index $1.2$. If both lenses are made of the same glass of refractive index $1.5$,the ratio of $f_1$ and $f_2$ will be:

In many experimental set-ups,the source and screen are fixed at a distance $D$ and the lens is movable. Show that there are two positions for the lens for which an image is formed on the screen. Find the distance between these points and the ratio of the image sizes for these two points.

$A$ convex lens is dipped in a liquid whose refractive index is equal to the refractive index of the lens. Then its focal length will

$A$ 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: