$A$ candle placed $25 \ cm$ from a lens forms an image on a screen placed $75 \ cm$ on the other side of the lens. The focal length and type of the lens should be

The diameter of a plano-convex lens is $6 \ cm$ and its thickness at the centre is $3 \ mm$. If the speed of light in the material of the lens is $2 \times 10^8 \ m/s$,find the focal length of the lens in $cm$.

The refractive index of the material of a double convex lens is $1.5$ and its focal length is $5 \,cm$. If the radii of curvature are equal, the value of the radius of curvature (in $cm$) is

Write the equation and definition of lateral magnification for a lens.

$A$ lateral object of height $h_o = 0.5\, cm$ is placed on the optical axis of a bi-convex lens of focal length $f = 80\, cm$,at an object distance $u = -60\, cm$. The image formed is:

In an optics experiment,with the position of the object fixed,a student varies the position of a convex lens and for each position,the screen is adjusted to get a clear image of the object. $A$ graph between the object distance $|u|$ and the image distance $|v|$,from the lens,is plotted using the same scale for the two axes. $A$ straight line passing through the origin and making an angle of $45^{\circ}$ with the $x$-axis meets the experimental curve at $P$. The coordinates of $P$ will be