$A$ double convex lens has two surfaces of equal radii $15 \, cm$ and refractive index $\mu = 1.5$. Its focal length is equal to ..... $cm$.

Refractive index of a glass convex lens is $1.5$. The radius of curvature of each of the two surfaces of the lens is $40 \text{ cm}$. The ratio of the power of the lens when immersed in a liquid of refractive index $1.25$ to that when placed in air is

Five persons $P_1, P_2, P_3, P_4$ and $P_5$ recorded object distance $(u)$ and image distance $(v)$ using the same convex lens having power $+5 \ D$ as $(25, 96), (30, 62), (35, 37), (45, 35)$ and $(50, 32)$ respectively. Identify the correct statement.

The focal length of a thin biconvex lens is $20 \ cm$. When an object is moved from a distance of $25 \ cm$ in front of it to $50 \ cm$,the magnification of its image changes from $m_{25}$ to $m_{50}$. The ratio $\frac{m_{25}}{m_{50}}$ is

The word $KVPY$ is written on a board and viewed through different lenses such that the board is at a distance beyond the focal length of the lens. Ignoring magnification effects,consider the following statements:
$(I)$ First image has been viewed from the planar side of a plano-convex lens and second image from the convex side of a plano-convex lens.
$(II)$ First image has been viewed from the concave side of a plano-concave lens and second image from the convex side of a plano-convex lens.
$(III)$ First image has been viewed from the concave side of a plano-concave lens and second image from the planar side of a plano-convex lens.
$(IV)$ First image has been viewed from the planar side of a plano-concave lens and second image from the convex side of a plano-convex lens.
Which of the above statements are correct?

The figure shows a convex lens cut symmetrically into two equal halves and separated laterally by a distance $h$. $A$ point object placed at a distance $30\, cm$ from the lens halves forms two real images separated by a distance $d$. $A$ plot of $d$ versus $h$ is shown in the figure. The focal length of the lens is ......$cm$.