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Concave Mirror

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Mirrors are usually made of a sheet of glass that is coated with a thin layer of shiny metal on one surface. A mirror with a flat surface is a plane mirror. If the surface is spherical or curved, it is known as curved mirror. An image is a copy of an object formed by rays of light. A plane mirror always produces a virtual image. A virtual image is a copy of an object formed at the location from which the light rays appear to come.

It is important however, to realize that the rays do not really come from behind the mirror. Sometimes you see images that are very distorted. Look into both side sides of a polished metal spoon. The images you see are quite different from the image formed by a plane mirror. Each side of the spoon produces a different image because each side is curved differently. The curved surface of the spoon changes the way light is reflected.

Definition

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When the inside surface of a curved mirror is the reflecting surface, the mirror is a concave mirror. The curvature of the reflecting surface causes the rays to come together. The point at which the light rays meet is called the focal point. Concave mirrors can form either real or virtual images. A real image is a copy of an object formed at the point where light rays actually meet. Unlike a virtual image, a real image can be viewed on a surface such as a screen.

Equation

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The general formula for mirrors and lenses to find out the focal length is,

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

or,

f = $\frac{uv}{u+v}$
where,
f
is the focal length,
u is the distance between the object and mirror,
v is the distance between the image and mirror.

The sign of the image will depends on where it is produced.

Ray Diagram

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As mentioned before, concave mirror produces both real and virtual images. The type of image formed depends upon where the object is in relation to the mirror. The image is formed at different position of the mirror according to the object's position. If the object is farther from the focal point, a real image is produced. If the object is near to the focal point, virtual image is produced. The ray diagrams of concave mirror is given below:

Concave Mirror Image Formation
Concave mirrors are often used in automobile headlights and flashlights to direct the illumination from a single light bulb into a beam. If the bulb is placed at the focal point of a concave mirror, the reflected light rays will be parallel to one another. This results in a brighter beam of light. Large concave mirrors are used to focus the solar light for energy production.

Examples

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Example problems related to concave mirror is described below:

Solved Examples

Question 1: Calculate the focal length of concave mirror if the image is formed at a distance 10cm when the object is at a distance 5cm?

Solution:
 
From the question it is given that,
u = 5cm and v = 10cm

The equation for focal length is,
f = $\frac{uv}{u+v}$

f = $\frac{5\times10}{5+10}$

f = $\frac{50}{15}$ = 3.33cm

 

Question 2: Calculate the focal length of concave mirror if the image is formed at a distance 25cm when the object is at a distance 10cm?

Solution:
 
From the question it is given that,
u = 10cm and v = 25cm

The equation for focal length is,
f = $\frac{uv}{u+v}$

f = $\frac{10\times25}{10+25}$

f = $\frac{250}{35}$ = 7.14cm