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Q48
(NDA-I/2022)
Science & Technology › Basic Science (Physics, Chemistry, Biology) › Geometrical optics
Answer Verified
What is the magnification produced by a concave lens of focal length 10 cm, when an image is formed at a distance of 5 cm from the lens?
Result
Your answer:
—
·
Correct:
C
Explanation
To find the magnification, we use the lens formula: 1/f = 1/v - 1/u. According to the sign convention, a concave lens has a negative focal length (f = -10 cm) [1]. Concave lenses always form virtual, upright, and diminished images on the same side as the object, so the image distance (v) is -5 cm. Substituting these values into the formula: 1/(-10) = 1/(-5) - 1/u. This simplifies to -1/10 = -2/10 - 1/u, which gives 1/u = -1/10, so the object distance (u) is -10 cm. Magnification (m) is defined as the ratio of image distance to object distance (m = v/u). Thus, m = (-5) / (-10) = 0.5. This positive value indicates a virtual and upright image, consistent with the properties of concave lenses.
Sources
- [1] Science , class X (NCERT 2025 ed.) > Chapter 9: Light – Reflection and Refraction > 9.3.6 Sign Convention for Spherical Lenses > p. 155
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