Mirror Formula

A security mirror in the car park of a building is $4 \mathrm{m}$ away from a Porsche car. If the mirror produced one-ninth magnification, calculate the radius of curvature of the mirror.

The mirror formula gives the relationship between the object distance, the image distance and the focal length in case of spherical mirrors. It is mathematically represented as:

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

Where, $u=$object distance, $v=$ image distance and $f=$focal length

The image produced by a spherical mirror can be larger than the object, smaller than the object or of the same size as the object depending upon the position of the object and the type of spherical mirror. The size of the image relative to the object is given by the linear magnification, $m$ given by the formula:

$m=\frac{h\text{'}}{h}$

Where, $h$ is the object height and $h\text{'}$ is the image height.

Now consider the following situation:

A $4 \mathrm{cm}$-long object is placed at a distance of $16 \mathrm{cm}$ in front of a concave mirror. The image formed is $6 \mathrm{cm}$ long and is real.

On the basis of the above information and what you have learnt in the course, answer the following question:

What is the focal length of the mirror?

The mirror formula gives the relationship between the object distance, the image distance and the focal length in case of spherical mirrors. It is mathematically represented as:
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
Where, $u=$object distance, $v=$ image distance and $f=$focal length
The image produced by a spherical mirror can be larger than the object, smaller than the object or of the same size as the object depending upon the position of the object and the type of spherical mirror. The size of the image relative to the object is given by the linear magnification, $m$ given by the formula:
$m=\frac{h\text{'}}{h}$
Where, $h$ is the object height and $h\text{'}$ is the image height.
Now consider the following situation:
A $4 \mathrm{cm}$-long object is placed at a distance of $16 \mathrm{cm}$ in front of a concave mirror. The image formed is $6 \mathrm{cm}$ long and is real.
On the basis of the above information and what you have learnt in the course, answer the following question:

Where is the image formed?

The mirror formula gives the relationship between the object distance, the image distance and the focal length in case of spherical mirrors. It is mathematically represented as:

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

Where, $u=$object distance, $v=$ image distance and $f=$focal length

The image produced by a spherical mirror can be larger than the object, smaller than the object or of the same size as the object depending upon the position of the object and the type of spherical mirror. The size of the image relative to the object is given by the linear magnification, $m$ given by the formula:

$m=\frac{h\text{'}}{h}$

Where, $h$ is the object height and $h\text{'}$ is the image height.

Now consider the following situation:

A $4 \mathrm{cm}$-long object is placed at a distance of $16 \mathrm{cm}$ in front of a concave mirror. The image formed is $6 \mathrm{cm}$ long and is real.

On the basis of the above information and what you have learnt in the course, answer the following question:

What is the magnification produced?

The mirror equation holds only when the aperture of the mirror is small.

A convex mirror used in a bus has a radius of curvature of $3.5 \mathrm{m}$. The driver of the bus locates a truck $10 \mathrm{m}$ behind the bus. Find the position, nature and size of image of the truck.

An object $3 \mathrm{cm}$ high is placed at a distance of $10 \mathrm{cm}$ in front of a concave mirror of focal length $20 \mathrm{cm}$. Find the position, nature and size of image formed.