Question

A point object is placed at a distance of $30\mathrm{cm}$ from a convex mirror of focal length of $30\mathrm{cm}$. The image will form at________

Answer 1

Step 1. Given data

1. According to the sign convention in mirror, the object distance $\mathrm{u}=-30\mathrm{cm}$,
2. Focal length $\mathrm{f}=30\mathrm{cm}$
3. We have to find image distance $\mathrm{v}$.

Step 2. Formula to be used.

Mirror formula:

1. A mirror can be made by silvering a metal surface with glass in front and paint at its back.
2. The mirror formula represent the relation between focal length, image distance and object distance,

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

Here, $\mathrm{f}$ is focal length, $\mathrm{v}$ is the distance of the image from the mirror and $\mathrm{u}$ is the distance of the object from the mirror.

Step 3. Calculate the image distance.

Now, by using the mirror formula, we get,

$\frac{1}{30}=\frac{1}{-30}+\frac{1}{\mathrm{v}}$

$\frac{1}{\mathrm{v}}=\frac{1}{30}+\frac{1}{30}$

$\frac{1}{\mathrm{v}}=\frac{2}{30}$

$2\mathrm{v}=30$

$\mathrm{v}=15$

1. The sign obtained is positive and the image distance is $15\mathrm{cm}$.
2. According to the sign convention in mirror, the image is formed $15\mathrm{cm}$ behind the mirror.

Hence, A point object is placed at a distance of $30\mathrm{cm}$ from a convex mirror of focal length of $30\mathrm{cm}$. The image will form at $15$ cm behind the image.