Question

When an object is placed in front of a concave mirror at a distance \[30\] cm from an image is obtained on a screen at a distance of \[20\] cm from the mirror. Find the focal length of the mirror.

Answer 1

Hint:The focal length of a concave mirror is positive, while that of a convex mirror is negative.A concave mirror is a spherical mirror with an inwardly curved reflective surface that meets the laws of light reflection. Light rays from a faraway object may be thought of as being parallel to one another.

Complete step by step answer:
The parallel rays of light reach the point in front of the mirror if the image produced is true, reversed, and very small in size. The picture created by the convex lens is real and can be seen on a monitor. The disparity between the principal axis $P$ and the focus $F$ of the concave mirror is denoted by the letter $f$.

From the question, we can analyze that it is given that we know that objects are often positioned on the left side of the mirror, or in the direction opposite to the incidence ray. As a result, the distance between objects will always be negative.
\[{\text{ u= - 30cm}}\]
and
\[{\text{f = - 20cm}}\]
By using mirror formula,
\[\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}\]
So substitute the values now.
\[\dfrac{1}{-20}+ \dfrac{1}{-30} = \dfrac{1}{f} \\
\therefore {\text{f = - 12}}\,{\text{cm}} \]

Hence, the focal length of the mirror is -12 cm.

Note:A concave mirror has a negative focal length, whereas a convex mirror has a positive focal length. You may also use the mirror formula (\[{\text{1/v + 1/u = 1/f}}\]) to show the same thing.