A convex lens of focal length 30 cm is placed in contact with a concave lens of focal length 20 cm. An object is placed at 20 cm to the left of this lens system. The distance of the image from the lens in cm is ________.

Solution

Physics sir · 3 steps

Replace the two lenses with one equivalent lens first, then apply the lens formula only once.

1. Combine the lenses. For thin lenses in contact, the powers add: 1/F = 1/f₁ + 1/f₂. With sign convention, the convex lens has f₁ = +30 cm and the concave lens has f₂ = -20 cm.

   1/F = 1/30 - 1/20 = (2-3)/60 = -1/60 ⇒ F = -60 cm

2. Apply lens formula. The system acts as a diverging lens of focal length 60 cm. The object is on the left, so u = -20 cm. Then 1/v = 1/F + 1/u = -1/60 - 1/20 = -4/60.
3. So. v = -15 cm. The image is virtual and forms on the same side as the object, 15 cm from the lens, which is option (b).

The idea to keep. For lenses in contact, add powers with signs: convex positive, concave negative. Then treat the pair as one lens and apply 1/v - 1/u = 1/f once.

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