Optics

Calculate the combined focal length of two thin lenses of focal length $f_1$ and $f_2$ separated by a finite distance $d$. Also find the position of two principal points.

Two thin converging lenses of focal lengths $20\,\mathrm{cm}$ and $30\,\mathrm{cm}$ respectively are placed co-axially in air and separated by a distance of $10\,\mathrm{cm}$. An object is located $60\,\mathrm{cm}$ in front of lens of smaller focal length. Find the position of principal points and the image.

Two thin converging lenses of focal lengths $30\,\mathrm{cm}$ and $40\,\mathrm{cm}$ respectively are placed coaxially in air and separated by a distance of $10\,\mathrm{cm}$. An object is placed $20\,\mathrm{cm}$ in front of the lens. Find the position and nature of final image.