$A$ magnifying lens has a focal length of $10 \, cm$. If the image is formed at a distance of $30 \, cm$ from the lens,what is the magnification?

$A$ beam of light converges at a point $P$. Now a lens is placed in the path of the convergent beam $12 \, cm$ from $P$. At what point does the beam converge if the lens is a convex lens of focal length $20 \, cm$ (in $, cm$)?

The far point of a nearsighted person is $6.0 \, m$ from her eyes,and she wears contact lenses that enable her to see distant objects clearly. $A$ tree is $18.0 \, m$ away and $2.0 \, m$ high. How high is the image formed by the contact lenses?

$A$ bi-concave glass lens having refractive index $1.5$ has both surfaces of same radius of curvature $R$. On immersion in a medium of refractive index $1.75$,it will behave as a

The focal length of an equi-convex lens is greater than the radius of curvature of any of the surfaces. Then the refractive index of the material of the lens is

$A$ plano-convex lens has a diameter of $6\, cm$ and a thickness of $3\, mm$ at the center. If the speed of light in the material of the lens is $2 \times 10^{8}\, m/s$,then the focal length of the lens is ..... $cm$.