In an experiment with a convex lens,the plot of the image distance $(v')$ against the object distance $(u')$ measured from the focus gives a curve $v' u' = 225$. If all the distances are measured in $cm$,the magnitude of the focal length of the lens is $cm$.

$A$ thin convex lens is made of a material of refractive index $1.6$. An object is kept at a distance of $u$ from the lens on the principal axis as shown in the figure. The radii of curvature of the surfaces are $10 \, cm$ and $5 \, cm$. Now,the lens is reversed such that the face having radius of curvature $5 \, cm$ lies close to the object. The difference in image position as obtained for both the cases is equal to ......$u$.

Explain the first focal centre (first principal focus) and second focal centre (second principal focus) for a biconvex lens and a biconcave lens with the help of diagrams.

$A$ bi-concave symmetric lens made of glass has a refractive index of $1.5$. It has both surfaces with the same radius of curvature $R$. On immersion in a liquid of refractive index $1.75$,it will behave as a:

$A$ 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 $1.5]$

$A$ screen is placed $90 \; cm$ from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by $20 \; cm$. Determine the focal length (in $cm$) of the lens.