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1800-102-2727Do you know which mirror is installed in your car as a side rearview mirror? In the car or vehicle, our requirement is to look at a wide area of the rear. Generally, we have three types of the mirror; plane mirror, concave mirror and convex mirror. All of them have different properties and hence different uses. In three of them, the convex mirror has the ability to make a virtual image of a small size. Hence we use a concave mirror in our cars so as to cover a larger rear area and to form a diminished image. Let's understand more about how it works!
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Spherical mirrors are curved glass plates which are painted with a reflecting material like silver on one of the sides and the other side is used for the reflection. This spherical mirror can be of two types: one is a concave mirror and the other is a convex mirror. The spherical glass plates which are painted outward and the inner surface used for the reflection are the concave mirrors. The spherical glass plates which are painted from the inside and the outer surface used for the reflection are the convex mirrors.
The part of the hollow sphere which is silver painted from the inside and the outer surface is used for the reflection purpose and is known as a convex mirror. The figure shows a convex mirror.
A convex mirror has the following properties:
These are the following terms related to the convex mirror.
To trace the image of an object there are certain rules which help in locating the image.
Regardless of the object's position, the image created by a convex mirror is always virtual and upright. Let's examine the types of images created by convex mirrors in this part. There are two possibilities for the placing of an object to get an image.
The mirror formula is an equation that links focal length of the mirror, object distance and image distance. The equation is given as
$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$
Where,
u= The object's distance from the pole
v= The image's distance from the pole.
f= Focal length of the mirror
The height ratio of the image to the object is known as magnification. It is given as,
$m=\frac{Heightofimage\left({h}_{i}\right)}{Heightofobject\left({h}_{o}\right)}$
If u is the distance of the object from the mirror and v is the distance of the image then the magnification can be written as
$m=\frac{{h}_{i}}{{h}_{o}}=-\frac{v}{u}$
Sign convention : Distance measured in the direction of the incident ray is taken as positive and opposite to this direction is taken as negative. The distance in upward direction to the principal axis is taken as positive and the distance measured in downward direction is taken as negative.
The convex mirror can be used for the following purposes-
Q1. When an object is positioned 40 cm in front of a mirror, a virtual image appears at 20 cm behind the mirror. Determine the kind and focal length of the mirror.
Answer. Given, the distance of object u= -40 cm
Distance of image v=20 cm
Using the mirror formula,
$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$
$\frac{1}{f}=\frac{1}{-40}+\frac{1}{20}$
$\frac{1}{f}=\frac{1}{20}-\frac{1}{40}$
$\frac{1}{f}=\frac{2-1}{40}$
$\frac{1}{f}=\frac{1}{40}$
f=40 cm
Focal length of mirror is 40 cm. Since the focal length is positive, the mirror is convex.
Q2. A convex mirror with a focal length of 20 cm is placed 20 cm away from a point object. Find the image location.
Answer. Given,
The distance object from the mirror, u=-20 cm
The mirror's focal length, f=20 cm
According to the mirror formula,
$\frac{1}{\mathit{f}}=\frac{1}{\mathit{u}}+\frac{1}{\mathit{v}}$
$\frac{1}{20}=\frac{1}{-20}+\frac{1}{\mathit{v}}$
$\frac{1}{\mathit{v}}=\frac{1}{20}+\frac{1}{20}$
$\frac{1}{\mathit{v}}=\frac{2}{20}$
$\frac{1}{\mathit{v}}=\frac{1}{10}$
v=10
The image is located 10 cm behind the mirror.
Q3. A 10 cm height object is placed in front of a convex mirror and forms an image of height 3 cm. Find the magnification of the mirror.
Answer. As we know the convex mirror always forms an erect image.
Given ${h}_{i}=+3cm$ and ${h}_{o}=+10cm$
The magnification by the mirror is given as,
$m=\frac{{h}_{i}}{{h}_{o}}$
$m=\frac{+3cm}{+10cm}$
m=0.3
Hence the magnification by the convex mirror is 0.3
Q4. A convex mirror forming an image at a distance of 15 cm behind the mirror. If an object is placed at a distance of 45 cm in front of the mirror, what is the magnification of the mirror?
Answer. Given v=+15 cm and u=-45 cm
The magnification of the mirror is given as,
$m=-\frac{v}{u}$
$m=-\frac{+15}{-45}$
m=0.33
Hence the magnification of the mirror is 0.33.
Q1. Why is the convex mirror used in street lights?
Answer. As the convex mirror diverges the light rays which fall on it, when a source is placed in front of the convex mirror it diverges the incident rays to a wider area. Hence more area can be lightened with a small light source.
Q2. What is a diverging mirror?
Answer. The mirror which diverges the light rays outward is called a diverging mirror. They do not focus the light to a point as happens in the case of converging mirrors. A convex mirror is an example of a diverging mirror.
Q3. How will you differentiate a convex mirror from a concave one?|
Answer. When an object is placed in front of a concave mirror, either it will form a real image of a large object. On the other hand, a convex mirror always forms a virtual image of diminished size.
Q4. Why is the magnification of the convex mirror positive and less than one?
Answer. As the convex mirror always forms an erect image i.e. the height of the image is in the same direction as that of the object with respect to the principal axis, it is positive. Also, the image formed by the convex mirror is diminished or smaller in size so the magnification will always be less than one.