Reflection by Spherical Mirrors: Practice Problem & Solution
An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, the displacement of the image will be: (2018)
Short Solution (Best for NEET):
To solve this problem, we apply the core principles of Reflection by Spherical Mirrors. Understanding the underlying formula is key to arriving at the correct answer below:
Initially $u_1 = -40 cm$ , $f = -15 cm$ . Using mirror formula, $v_1 = \frac{u_1 f}{u_1 - f} = \frac{(-40)(-15)}{-40 - (-15)} = \frac{600}{-25} = -24 cm$ . After moving 20 cm towards the mirror, $u_2 = -20 cm$ . The new image position is $v_2 = \frac{(-20)(-15)}{-20 - (-15)} = \frac{300}{-5} = -60 cm$ . Displacement is $v_2 - v_1 = -60 - (-24) = -36 cm$ , meaning 36 cm away from the mirror.
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