The same size images are formed by a convex lens when the object is placed at $20\, cm$ or at $10\, cm$ from the lens. The focal length of the convex lens is ............ $cm$.

In the displacement method of a lens,we obtain two images for different positions of the lens. One image is magnified,and the other is diminished. If $m$ is the magnification of the first image,then the focal length of the lens is given by:

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

Letters $A, B, C$ and $D$ are written on a cardboard as shown in the figure. The cardboard is kept at a suitable distance behind a transparent empty glass of cylindrical shape. If the glass is now filled with water,one sees an inverted image of the pattern on the cardboard when looking through the glass. Ignoring magnification effects,the image would appear as:

The image of an object,formed by a plano-convex lens at a distance of $8 \ m$ behind the lens,is real and is one-third the size of the object. The wavelength of light inside the lens is $\frac{2}{3}$ times the wavelength in free space. The radius of the curved surface of the lens is: (in $m$)

$A$ thin equiconvex lens is made of glass of refractive index $1.5$ and its focal length is $0.2 \ m$. If it acts as a concave lens of $0.5 \ m$ focal length when dipped in a liquid,the refractive index of the liquid is: