JEE Main 2021 · 27 August · morning · Single correct · +4 / −1

Find the distance of the image from object O, formed by the combination of lenses in the figure :

JEE Main PYQ figure
  1. (a) 75 cm
  2. (b) 10 cm
  3. (c) 20 cm
  4. (d) infinity
Answer and solution

Answer (a) 75 cm

Solution

Physics sir · 4 steps

Pass the light through one lens at a time, and let each image become the next lens's object.

  1. 1/v - 1/u = 1/f

  2. First lens. With u = -30 cm and f = +10 cm, we get 1/v = 1/10 - 1/30 = 1/15, so v = +15 cm. This image lies 15 cm to the right of the first lens.
  3. Second lens. The diverging lens is only 5 cm away, so the light meets it before forming that image. The image is 10 cm beyond it and acts as a virtual object with u = +10 cm. Then 1/v = -1/10 + 1/10 = 0, so v = ∞ and the light leaves as a parallel beam.
  4. Third lens. A parallel beam is focused at the focal point. The final image forms 30 cm to the right of the f = +30 cm lens.
  5. So. The distance from O is 30 + 5 + 10 + 30 = 75 cm, which is option (a).

The idea to keep. For a lens system, solve lens by lens and shift the origin each time. If an image falls beyond the next lens, it becomes a virtual object with positive u.

Answer from the NTA final answer key. Solution by PrepWiser.

Study Ray Optics

Asked about 200 times in JEE Main since 2020. This question is from 2021.