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

$A$ 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.

$(i)$ If $f=0.5 \,m$ for a glass lens,what is the power of the lens?
$(ii)$ The radii of curvature of the faces of a double convex lens are $10 \,cm$ and $15 \,cm$. Its focal length is $12 \,cm$. What is the refractive index of glass?
$(iii)$ $A$ convex lens has $20 \,cm$ focal length in air. What is its focal length in water? (Refractive index of water $= 1.33$,refractive index of glass $= 1.5$)

The focal lengths of a converging lens are $f_V$ and $f_R$ for violet and red light,respectively. Which of the following relations is correct?

Provide the object distance,image distance,type,size,and magnification for an object placed in front of a thin convex lens for different positions.

The focal length of a convex lens is $10 \ cm$ and its refractive index is $1.5$. If the radius of curvature of one surface is $7.5 \ cm$,the radius of curvature of the second surface will be......$cm$.