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 the material of the lens?

$A$ rod of length $2 \text{ cm}$ makes an angle of $\frac{2 \pi}{3} \text{ rad}$ with the principal axis of a thin convex lens. The lens has a focal length of $10 \text{ cm}$ and is placed at a distance of $\frac{40}{3} \text{ cm}$ from the object as shown in the figure. The height of the image is $\frac{30 \sqrt{3}}{13} \text{ cm}$ and the angle made by it with respect to the principal axis is $\alpha \text{ rad}$. The value of $\alpha$ is $\frac{\pi}{n} \text{ rad}$,where $n$ is:

Explain the first focal point and second focal point for a lens.

For a convex lens,if a real image is formed,the graph between $(u + v)$ and $u$ or $v$ is as follows:

$A$ lens of refractive index $n$ is placed in a liquid of refractive index $n'$. If the focal length of the lens in air is $f$,what will be its focal length in the liquid?

$A$ 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 $, cm$)?