A convex lens L₁ of focal length +10 cm is followed by a concave lens L₂ of focal length -10 cm, 3 cm to its right. A real object lies 30 cm to the left of L₁. Find the final image position relative to L₂. Image
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Question

A convex lens L₁ of focal length +10 cm is followed by a concave lens L₂ of focal length -10 cm, 3 cm to its right. A real object lies 30 cm to the left of L₁. Find the final image position relative to L₂. Image

Options

G1 Physics · Accepted Answer

Step 1: Apply lens equation 1/v₁ − 1/u₁ = 1/f₁ with u₁ = −30 cm and f₁ = +10 cm. Step 2: 1/v₁ = 1/10 − 1/30 = 1/15, so v₁ = +15 cm from L₁. Step 3: Since L₂ is 3 cm right of L₁, the would-be image is 12 cm to the right of L₂. For L₂ this is a virtual object: u₂ = +12 cm. Step 4: For L₂ (f₂ = −10 cm), 1/v₂ − 1/12 = −1/10, hence 1/v₂ = −1/10 + 1/12 = −1/60. Step 5: v₂ = −60 cm, indicating the final image lies to the left of L₂. Final answer: 60 cm left of the concave lens (Option B).

A convex lens L₁ of focal length +10 cm is followed by a concave lens L₂ of focal length −10 cm, 3 cm to its right. A real object lies 30 cm to the left of L₁. Find the final image position relative to L₂. Image