Question

A concave mirror produces a three times enlarged image of an object placed at 10cm in front of it. Calculate the focal length of the mirror.

Answer 1

Hint: The size of the image formed in the concave mirror depends on the position of the object from the center of the mirror and its focal length. Calculate the image distance by rearranging the magnification formula. Using this image distance and given object distance calculate the focal length of the concave mirror.

Complete step-by-step answer:
Consider the parallel beam of light incident on the concave mirror that they are parallel and incident at points close to the bone disease are reflected and passed through a common point also known as principal axis. This point is called the focal point and is known as the principal focus of a concave mirror. It is distance from the pole is called the focal length of (f) mirror
For the concave mirror, the focal length f is given by
f = R/2
Where R is the radius curvature of the mirror.
Given that the image is three-time larger than original. Object distance is 10cm. Magnification (m) is 3.
m = 3, u = 10
We know that magnification is given by,
$\begin{align}
  & m=\dfrac{-v}{u} \\
 & 3=\dfrac{-v}{10} \\
 & v=-30cm \\
\end{align}$
 Hence image distance is 30cm.
According to mirror formula,
\[\dfrac{1}{f}=\dfrac{1}{u}+\dfrac{1}{v}\]
Where,
u = object distance
v = image distance
Now put the value of u and v in the mirror formula.
\[\]\[\begin{align}
  & \dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u} \\
 & \dfrac{1}{f}=\dfrac{1}{30}-\dfrac{1}{10} \\
 & f=-15cm \\
\end{align}\]

Note: If the parallel beam is incident with some angle with principal axis the reflected rays converge at a point in a plane through normal to a principal axis this plane is called focal plane of the mirror. Take care of the sign of image distance and object distance while calculation.