Correct Answer - Option 1 : 0.1 m
CONCEPT:
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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 and virtual images of any object.
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Mirror formula: The expression which shows the relation between object distance (u), image distance (v), and focal length (f) is called the mirror formula.
\(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\)
Linear magnification (m):
- It is defined as the ratio of the height of the image (hi) to the height of the object (ho).
\(m = \frac{{{h_i}}}{{{h_o}}}\)
- The ratio of image distance to the object distance is called linear magnification.
\(m = \frac{{image\;distance\;\left( v \right)}}{{object\;distance\;\left( u \right)}} = - \frac{v}{u}\)
- A positive value of magnification means virtual an erect image.
- A negative value of magnification means a real and inverted image.
CALCULATION:
Given - f = 0.8 m, m = 4, let U = x
- The magnification of the image is given by
\(\Rightarrow 4 = -\frac{V}{u}\)
\(\Rightarrow V = -4x\)
Substituting the value of V and u in the equation for focal length
\(\Rightarrow \frac{1}{f} = -\frac{1}{x}- \frac{1}{4x} = \frac{-5x}{4x^{2}}\)
\(\Rightarrow f = - \frac{4x^{2}}{5x} = -\frac{4x}{5}\)
\(\Rightarrow x = \frac{-5\times f}{4} =- \frac{-5\times 0.8}{4} = -0.1 m\)
- Hence, the object must be placed at a distance of 10 cm away from it
- Hence, option 1 is the answer.