The Focal Length of a Convex Mirror

# The Focal Length of a Convex Mirror

## Introduction

A convex mirror is a curved mirror with a reflective surface that bulges out towards the light source. The light is reflected outwards by the convex mirror; hence it is not used to focus light. The size of the thing increases as it gets closer to the mirror until it achieves its original size. Diverging mirrors are another name for these mirrors. Because convex mirrors bounce light outwards, they are not utilized to concentrate light. Because the focal point (F) and the center of curvature (2F) are both hypothetical positions “within” the mirror that cannot be reached, such mirrors always produce a virtual image. As a result, the images created by these mirrors can’t be projected onto a screen because they’re too small.

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## A brief outline

A convex mirror’s image is always decreased (smaller), upright, and virtual (rays don’t actually travel through the image; their extensions do, as in a conventional mirror) (not inverted). The picture grows larger as the thing goes closer to the mirror until it reaches about the size of the object when it contacts the mirror. The image shrinks in size and gets closer to the focus as the object moves away until it is limited to a point in the focus whenever the object is at an infinite distance. These characteristics make convex mirrors extremely useful: because everything appears small in the mirror, they cover a larger field of view than a typical plane mirror, making them ideal for viewing behind a driver’s vehicle.

## Convex Mirror Focal Length Using Convex Lens

The convex mirror is a curved mirror with a bulging mirrored surface that faces the light source. Because a convex mirror reflects light outwards, it will not be used to focus light. A diverging mirror or fish-eye mirror is another name for a convex mirror. Because the focal point (F) and center of curvature (2F) are both hypothetical positions within the mirror that cannot be reached, the image formed by a convex lens is erect and virtual. As a result, because the image created by these mirrors is inside the mirror, it cannot be displayed on the screen. As a result, the focal length cannot be calculated directly.

The picture is initially smaller than the thing, but as the object near the mirror, it grows larger. A convex mirror’s focal length can be calculated by placing a convex lens between the item and the convex mirror. When the convex mirror bounces the rays along such a path, i.e. when rays fall normally on the mirror, an image can be obtained with the use of a convex lens side by side with an item. The radius of curvature, represented as R, is the distance between both the screen and the mirror.

The focal length f of the convex mirror can be computed using the formula below.

Where,

F = R/2

A Convex mirror has a reflecting surface that faces outwards, whereas a concave mirror has a reflecting surface that faces inwards. The Convex mirror’s coating is on the outside of the spherical surface, while the concave mirror’s coating is on the inside. The primary emphasis of a Convex Mirror is behind it, whereas the primary focus of a Concave Mirror is in front. The principal focus is the place where the reflected rays meet or look to meet.

## The following approach can be used to determine the focal point of a Convex Lens:

1. Arrange the lens as well as the screen on the wooden chair.
2. The lens must be positioned on the holder such that it faces a faraway object.
3. The screen should be put on the bench with the holder.
4. The screen should be positioned so that it displays a clear view of the distant item.
5. The focal length of the specified convex lens must be equal to the distinction between the 2 places, i.e., the lens and the screen.
6. To compute the focal length of the convex lens, shift the focus to various other distant objects.

## Significance of focal length of the convex mirror in IIT JEE exam

For the IIT JEE exam, as well as reference in the future and competitive test preparation, the chapter on optics is vital. A few crucial points in this Chapter could not be overlooked. This chapter covers light reflection, convex and concave mirrors, and other subjects. The exam questions in this chapter are both numerical and definitional in nature. According to the chapter-by-chapter weighting allocation for the IIT JEE test, the focal length of the convex and concave mirror has been asked about 5% of the total questions in the past eight years’ exam pattern.

• The convex mirror offers a wide range of practical and scientific uses.
• Convex mirrors are placed at ATMs to alert customers if someone is approaching from behind. This is to ensure user security while using the ATM, prevent cash withdrawal theft, and protect the user’s identity.
• It is a material used in sunglasses to reflect light away from the person wearing them.
• Aside from that, it’s utilized in street lights to disperse light beams across a larger area and in telescopes to perceive distant things like stars.

## FAQ’s

##### What distinguishes a convex mirror?

We all have a plane mirror in our houses, where the image of the reflecting object is the same size as the thing itself. The reflected picture is magnified in a concave mirror. If the object is held far enough away from the mirror, a concave mirror can also produce an inverted picture. The convex mirror, on the other hand, will always produce a virtual, erect, and greatly reduced picture.

##### What characteristics does a convex mirror have?

Since the reflective surface bulges outwards in the path of the light rays, the convex mirror is also known as a curved, diverging, or fish-eyed mirror. As a result, the focus point and center of curvature are hidden behind the mirror, making them fictitious and impossible to reach.

##### What is the difference between a convex and a concave mirror?

The reflective surface of a concave mirror curls inward whereas a convex mirror bulges outward toward this source of light. A convex mirror produces an image that is smaller than the original size of the object, whereas a concave mirror produces an image that is larger than the actual size of the object.

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