Option 2 : 60 cm from the mirror on the side of the object
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Concept:
- Spherical mirrors are of two types - Convex mirror, and Concave mirror.
- The image formed by the spherical mirrors depends on the position of the object.
- The relationship between the focal length (f) and the radius of curvature (R) is given by -
\(f = \frac{R}{2}\)
- Concave mirror: If the inner surface of the spherical mirror is the reflecting surface, then it is called a concave mirror. It is also called a focusing mirror/converging mirror.
- The size of the image produced by these mirrors can be larger or smaller than the object, depending upon the distance of the object from the mirror.
- The concave mirror can form both real as well as virtual images of any object.
- Mirror formula: The expression which shows the relation between object distance (u), image distance (v), and focal length (f) is called mirror formula.
\(\frac{1}{f} = \frac{1}{u} + \frac{1}{v}\)
Calculation:
Given,
Radius of curvature of concave mirror (R) = -40 cm
So focus = R/2 = -40/2 = -20 cm
Object is placed in front of mirror (u) = -30 cm
Image position (v) =?
We know that,
\(\frac{1}{f} = \frac{1}{u} + \frac{1}{v} \Rightarrow \frac{1}{v} = \frac{1}{f} - \frac{1}{u}\)
\( \Rightarrow \frac{1}{v} = \frac{1}{{ - 20}} - \frac{1}{{ - 30}} = \frac{{ - 3 + 2}}{{60}} = - \frac{1}{{60}}\)
\(\frac{1}{v} = - \frac{1}{{60}} \Rightarrow v = - 60\;cm\)
The image is formed at 60 cm in front of mirror or on the side of object.
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A concave mirror is a part of a sphere of radius 40cm. What is the focal length of the mirror?
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