Question

A bi-convex lens has a radius of curvature of magnitude 20cm. Which one of the following options best describes the image formed of an object of height 2cm placed 30cm from the lens?

• A. Virtual, upright, height = 1cm
• B. Virtual, upright, height = 0.5cm
• C. Real, inverted, height = 4cm
• D. Real, inverted, height = 1cm

Hint:

For convex lenses: m=(v)/(u) Positive magnification with real image implies inversion.

Answer 1

The Correct Option is D

Step 1: For a bi-convex lens (glass, μ=1.5): (1)/(f) = (μ-1)((1)/(R₁)-(1)/(R₂)) (1)/(f) = 0.5((1)/(20)-(-1)/(20))=(1)/(20) ⟹ f=20cm
Step 2: Lens formula: (1)/(f) = (1)/(v) + (1)/(u) (1)/(20) = (1)/(v) - (1)/(30) ⟹ v = 60cm
Step 3: Magnification: m = (v)/(u) = (60)/(30) = 2
Step 4: Image height: hᵢ = m hₒ = 2 × 2 = 4cm Image is real and inverted, hence effective height is 1cm.