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JEE Main20198 Apr 2019Morning ShiftPhysicsRay OpticsActual

An upright object is placed at a distance of 40 c m in front of a convergent lens of focal length 20 c m . A convergent mirror of focal length 10 c m is placed at a distance of 60 c m on the other side of the lens. The position and size of the final image will be:

Options

  1. A40 c m from the convergent lens, twice the size of the object
  2. B20 c m from the convergent mirror, twice the size of the object
  3. C40 c m from the convergent lens, same size of the object
  4. D20 c m from the convergent mirror, same size of the object

Correct answer

C. 40 c m from the convergent lens, same size of the object

Step-by-step solution

First refraction, u = - 40   c m ;   f = + 20   c m From lens formula, 1 v - 1 u = 1 f 1 v - 1 - 40 = 1 20 ⇒ 1 v = 1 20 - 1 40 v = + 40   c m m 1 = - 1 First reflection, u = - 20   c m ; f = - 10   c m From mirror formula, 1 v + 1 u = 1 f 1 v - 1 20 = 1 - 10 1 v = 1 - 10 + 1 20 ⇒ v = - 20   c m m 2 = - 1 Second refraction, u = - 40   c m ,    f = + 20   c m From lens formula, 1 v - 1 - 40 = 1 20 ⇒ v = + 40   c m m 3 = - 1 m t o

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