Question

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

Answer 1

Concave Mirror

1. When a hollow spherical is divided into parts and the exterior surface of each cut portion is painted, it forms a mirror, with the inner surface reflecting the light.
2. A concave mirror is a name for this sort of mirror. When light strikes and reflects back from the concave mirror's reflecting surface, it converges at a point. As a result, it's also called a converging mirror.
3. A magnified, erect, and virtual picture is obtained when the concave mirror is put very close to the item.
4. When the distance between the item and the mirror is increased, however, the size of the picture shrinks, and a genuine and inverted image is generated.
5. The concave mirror can produce a little or huge picture, which can be real or virtual.

Mirror Equation

The object distance ($u$), image distance ($v$), and focal length ($f$) are all expressed quantitatively in the mirror equation. The following is the equation:$\frac{1}{\mathrm{u}}+\frac{1}{\mathrm{v}}=\frac{1}{\mathrm{f}}$

Step 1: Given data

$$\begin{gathered} \mathrm{u}=-30\mathrm{cm} \\ \mathrm{v}=-20\mathrm{cm} \end{gathered}$$

Step 2: Formula used

$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$

Step 3: Calculation

By substituting the values in the above formula, we get

$$\begin{gathered} \frac{1}{-30}+\frac{1}{-20}=\frac{1}{\mathrm{f}} \\ \mathrm{f}=-12\mathrm{cm} \end{gathered}$$

Therefore, the focal length of the mirror is $-12\mathrm{cm}$.