When an object is placed 40 cm from a spherical mirror, an image with magnification +1/2 is formed. To obtain an image with magnification +1/3, the object should be moved:
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Question

When an object is placed 40 cm from a spherical mirror, an image with magnification +1/2 is formed. To obtain an image with magnification +1/3, the object should be moved:

G1 Physics · Accepted Answer

For a spherical mirror, m = -v/u. Initially, u₁ = -40 cm, m₁ = +1/2. Thus, v₁ = -m₁u₁ = -(1/2)(-40) = +20 cm. Mirror formula: 1/f = 1/v₁ + 1/u₁ = 1/20 - 1/40 = 1/40. Hence, f = +40 cm. For the new magnification m₂ = +1/3: v₂ = -u₂/3. Using the mirror formula: 1/40 = 1/(-u₂/3) + 1/u₂ = -3/u₂ + 1/u₂ = -2/u₂. Therefore, u₂ = -80 cm. The object position changes from 40 cm to 80 cm from the mirror, so it must be moved 40 cm away. Correct option: B.