A double convex lens is used to couple a laser beam of diameter 5 mm into an optical fiber with a numerical aperture of 0.5. The minimum focal length of the lens that should be used in order to focus the entire beam into the fiber is

Q. Consider a 'beam expander' which consists of two converging lenses of focal lengths 40 cm and 100 cm having a common optical axis. A laser beam of diameter 2 mm is incident on the 40 cm focal length lens. Then what is the diameter (in mm) of the final beam (see figure)?

Q. Light coming out of an optical fiber is incident on a plane perpendicular to the fiber axis and 50 mm away from the end of the fiber. The light coming out creates a circular spot that can at most be of $20\text{mm}$ diameter. Neglecting the diameter of the fiber, the numerical aperture of the fiber is, approximately,

Q. A beam of a parallel rays is brought to a focus by a convex lens. If a thin concave lens of equal focal length is joined to the convex lens, the focus will be

Q. A convex lens of diameter $8cm$ is used to focus a parallel beam of light of wavelength $620nm$. Light is focused at a distance $20cm$, from the lens. What would be the radius of central bright fringe?

Q. A convex lens of focal length $20cm$ and a concave lens of focal length $10cm$ are placed $10cm$ apart with their principal axes coinciding. A beam of light travelling parallel to the principal axis and having a beam diameter $5.0mm$, is incident on the combination. Show that the emergent beam is parallel to the incident one. Find the beam diameter of the emergent beam.