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A plano convex lens of refractive index μ₁ and focal length f₁ is kept in contact with another plano concave lens of refractive index μ₂ and focal length f₂. If the radius of curvature of their spherical faces is R each and f₁=2f₂, then μ₁ and μ₂ are related as

Asked in JEE Main 10th Jan 1st Shift 2019 · Combinations and silvered lenses

• (1) 3μ₂-2μ₁=1
• (2) μ₁+μ₂=3
• (3) 2μ₁-μ₂=1
• (4) 2μ₂-μ₁=1

Step-by-step solution

Why the other options are wrong

• (1) Makes an algebra slip moving the factor 2.
• (2) Keeps the minus sign of f₂, which gives 2μ₁+μ₂=3, and then drops the factor 2.
• (4) Puts the factor 2 on the wrong lens (f₂=2f₁).

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