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

$A$ convex lens made of glass has a focal length of $0.15 \,m$ in air. If the refractive index of glass is $\frac{3}{2}$ and that of water is $\frac{4}{3}$, what is the focal length of the lens when immersed in water (in $\,m$)?

The sun's diameter is $1.4 \times 10^9 \ m$ and its distance from the earth is $10^{11} \ m$. The diameter of its image,formed by a convex lens of focal length $2 \ m$,will be.......$cm$.

$f_V$ and $f_R$ are the focal lengths of a convex lens for violet and red light respectively,and $F_V$ and $F_R$ are the focal lengths of a concave lens for violet and red light respectively. Then:

$A$ convex lens forming a real image of magnification $m_1$ on a screen is moved through a distance $x$. $A$ new image of magnification $m_2$ is again formed on the screen. The focal length of the lens is:

When an object of height $12 \ cm$ is placed at a distance from a convex lens, an image of height $18 \ cm$ is formed on a screen. Without changing the positions of the object and the screen, if the lens is moved towards the screen, another clear image is formed on the screen. The height of this image is (in $cm$)