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A car is fitted with a convex side-view mirror of focal length 20 cm. A second car 2.8 m behind the first car is overtaking the first car at a relative speed of 15 m s⁻¹. The speed of the image of the second car as seen in the mirror of the first one is

Asked in JEE Main 2011 · Mirror formula and magnification

• (1) 1/(10) m s⁻¹
• (2) 1/(15) m s⁻¹
• (3) 10 m s⁻¹
• (4) 15 m s⁻¹

Step-by-step solution

Why the other options are wrong

• (1) Makes a sign slip in the mirror formula, 1/v=1/(0.2)-1/(2.8), so v/u=1/(13) and the speed comes out near 1/(11)≈1/(10) m s⁻¹.
• (3) Scales the speed down only slightly; the image speed is the object speed times m²=1/(225), not a modest fraction.
• (4) Assumes the image moves at the same speed as the object.

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