An object is placed on the axis of a convex lens. Its image is formed $80 \, cm$ from the object. The magnification is $3$. The focal length of the lens is.....$cm$

$A$ biconvex lens has a focal length $2/3$ times the radius of curvature of either surface. The refractive index of the material is:

In an optical bench experiment, the index error is $+1 \, cm$ and $-1 \, cm$ between the object needle and lens, and between the lens and image needle, respectively. The observed values of $u$ and $v$ are $9 \, cm$ and $17 \, cm$. The focal length of the lens is ..... $cm$.

Consider an equi-convex lens of glass $\left( \mu = \frac{3}{2} \right)$. If the temperature of the lens is increased by $40\, ^\circ C$,its focal length remains the same. The coefficient of linear expansion of glass is $2.5 \times 10^{-4} / ^\circ C$. Calculate the change in the refractive index of the glass on increasing the temperature by $40\, ^\circ C$.

$A$ 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 concave lens of focal length $16 \, cm$ (in $, cm$)?

For a given lens,the magnification was found to be twice as large when the object was $0.15 \ m$ distant from it as when the distance was $0.2 \ m$. The focal length of the lens is.......$m$.