An object is placed at a distance of 40 cm from a convex lens of focal length 10 cm, such that an image is formed at a distance of X cm from the lens. What is the value of X?
+40/3
Correct Answer: +40/3
Using the lens formula: 1/v − 1/u = 1/f
- Object distance u = −40 cm (on the same side as the object, negative by sign convention)
- Focal length f = +10 cm (convex lens, positive)
1/v = 1/f + 1/u = 1/10 + 1/(−40) = 4/40 − 1/40 = 3/40
∴ v = +40/3 cm ≈ +13.3 cm
The positive sign indicates the image is formed on the opposite side of the object (real image). Since object is beyond 2F (40 > 2×10=20), the image is between F and 2F (real, inverted, diminished).
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