Correct Answer - Option 1 : Real and Enlarged image
CONCEPT:
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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).
i.e. \(m = \frac{{{h_i}}}{{{h_o}}}\)
- The ratio of image distance to the object distance is called linear magnification.
i.e. \(m = \frac{{image\;distance\;\left( v \right)}}{{object\;distance\;\left( u \right)}} = - \frac{v}{u}\)
CALCULATION:
Given that:
u = - 15 cm and f = - 10 cm
Mirror formula
\(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\)
\(\therefore \frac{1}{v} = \frac{1}{f} - \frac{1}{u} = - \frac{1}{{10}} + \frac{1}{{15}} = \frac{{ - 3 + 2}}{{30}} = - \frac{1}{{30}}\;cm\)
v = - 30 cm
Linear magnification (m)
\(m = - \frac{v}{u}\)
\(\Rightarrow m = - \frac{{\left( { - 30} \right)}}{{ - 15}} = - 2\)
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Enlarged image.
- Since the object is placed before the focal point. So image formed by the concave mirror is real.
- Thus the image is real and enlarged. Hence option 1 is correct.
- The image formed by the concave mirror will be virtual only when the object is placed between the focal point and the mirror.
