Question

A concave mirror has a radius of curvature \[40cm\] . At what distance from the pole of the mirror a parallel beam of light would be focused after reflection?

Answer 1

Hint: A concave mirror has a reflecting surface that is curved inwards (away from the incident light). Concave mirrors converge light inward to the principal focus. They are used to focus light. In contrast to convex mirrors, concave mirrors produce images of different types depending on the location of the object on the principal axis.

Formula used: \[f=\dfrac{R}{2}\]

Complete solution:
As discussed above, light rays incident parallel to the principal axis of a concave mirror converge at a particular point after reflecting from the mirror, known as the principal focus of the mirror.
We have been told that the radius of curvature of the mirror is \[40cm\] , that is \[R=40cm\]
The light rays will converge at the principal focus of the mirror. From the definition of principal focus, it is at a distance equal to half the radius of curvature of the mirror from the pole of the mirror.
Thus, the principal focus \[f=\dfrac{40cm}{2}=20cm\].

Hence the rays will converge at a distance of \[20cm\] from the pole of the mirror.

Note: Concave mirrors are used in reflecting telescopes. Concave mirrors are also used in salons to provide a magnified view of the face for shaving. Illuminating devices use concave mirrors to collect light from the source and direct it outward in a beam as in torches, headlamps and spotlights, or to do the opposite, that is, collect light from a larger area and focus it into a smaller space, as in solar cookers. Concave mirrors form cavities, which are important in the construction of a laser. Dentists use a concave surface to provide an enlarged image.