The focal lengths for violet,green,and red light rays are ${f_V}$,${f_G}$,and ${f_R}$ respectively. Which of the following is the true relationship?

Write the lens maker's equation for a thin lens.

The refractive index of a converging lens is $1.4$. What will be the focal length of this lens if it is placed in a medium of the same refractive index? (Assume the radii of curvature of the faces of the lens are $R_{1}$ and $R_{2}$ respectively)

$A$ point source of light is moving at a rate of $2 \,cm \,s^{-1}$ towards a thin convex lens of focal length $10 \,cm$ along its optical axis. When the source is $15 \,cm$ away from the lens,the image is moving at:

$A$ glass convex lens $(\mu_g = 1.5)$ has a focal length of $8\, cm$ in air. What will be its focal length when it is immersed in water (in $, cm$)? $(\mu_w = 1.33)$

$A$ point source is located at a distance of $20 \ cm$ from the front surface of a symmetrical glass biconvex lens with equal radii of curvature $5 \ cm$. The distance at which the image is formed from the rear surface of this lens is $[$Given refractive index of the glass is $1.5]$