Question

: A doctor looks through a small hole at the vertex of a concave mirror to examine a sore throat. If the radius of curvature of the mirror is 40 cm and the light source is 1 m from the mirror, the distance from the throat should the mirror be if the light is to be imaged on the inflamed area is:
(A) 50 cm
(B) 25 cm
(C) 40 cm
(D) 20 cm

Answer 1

Hint: We all know that a concave mirror is that part of the reflecting sphere where we perceive that the reflecting element is far away from the incident rays of the body. A concave mirror is used generally in terrestrial telescopes and disease diagnosis instruments.

Complete step by step answer:
We should write the given data according to the sign convention.
The radius of curvature of the mirror is $R = 40\;{\rm{cm}}$.
We know that the focal length of the mirror is $f = - \dfrac{R}{2}$.
We will now substitute $R = 40\;{\rm{cm}}$ for finding the focal length, and it becomes,
$\begin{array}{l} f = - \dfrac{{40\;{\rm{cm}}}}{2}\\\ = - 20\;{\rm{cm}} \end{array}$
The distance of the light source is u that is,
$\begin{array}{l} u = - 1\;{\rm{m}} \times \dfrac{{100\;{\rm{cm}}}}{{1\;{\rm{m}}}}\\\ = - 100\;{\rm{cm}} \end{array}$
We will now apply the mirror equation for this concave mirror. Hence it is,
$\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v}$
We will now substitute $f = - 20\;{\rm{cm}}$ and $u = - 100\;{\rm{cm}}$ to find the value of v.
$\begin{array}{l} \dfrac{1}{{ - 20\;{\rm{cm}}}} = \dfrac{1}{{ - 100\;{\rm{cm}}}} + \dfrac{1}{v}\\\ v = - 25\;{\rm{cm}} \end{array}$
Therefore, the distance at which the mirror is placed is 25 cm, and the correct option is (B).

Additional Information: We must also know about Convex mirror is a part of a hollow sphere having an inner part (depressed surface) silvered and the outer surface (bulging surface) as a reflecting surface. A convex mirror diverges the parallel beam of light, so it is called a diverging mirror. This mirror is also known as the driver’s mirror because it is used in the rear-view mirror. The convex mirror always produces a virtual image behind the mirror, which is erect, diminished. Always remember the mirror formula is the same for a concave and convex mirror.

Note: We know that the nature of the image formed in the concave mirror section is real and the size of the image is also tiny when the object is kept far away from the concave mirror, and the image is virtual when the body is close to the mirror.