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JEE Main 2021 (26 Aug, Shift 2) · Combination of Lenses

Combination of Lenses question from JEE Main 2021 (26 Aug, Shift 2)

Q49JEE Main 2021 · 26 AUG · SHIFT 2Difficult

Combination of Lenses

An object is placed at a distance of 12 cm from a convex lens. A convex mirror of focal length 15 cm is placed on other side of lens at 8 cm as shown in the figure. Image of object coincides with the object.

Figure

When the convex mirror is removed, a real and inverted image is formed at a position. The distance of the image from the object will be .............. (cm)

Numerical answer type. Work it out, then open the answer.

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Answer: 50

  1. Image coincides with the object, so rays from the lens hit the convex mirror normally: the lens image is at the mirror's centre of curvature.
  2. R=2f=30 cmR = 2f = 30\text{ cm}, so the lens image is 8+30=38 cm8 + 30 = 38\text{ cm} from the lens.
  3. Without the mirror the real inverted image is at this same point.
  4. Distance from the object: 12+38=50 cm12 + 38 = 50\text{ cm}.
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