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NCERT Class 10 Science Light – Reflection and Refraction: In-text questions (page 158) Solutions
AI-written, checked on 23 Oct 2026
Solutions written by Shishya, checked — not the board's official answers
Step-by-step working for every question of In-text questions (page 158) in NCERT's Class 10 Science book, chapter “Light – Reflection and Refraction”, written by Shishya. Each question is in our own short words; open the NCERT chapter for the exact wording and figures.
How these were checked: the solutions were drafted with AI and then read and corrected on 23 Oct 2026. Every numerical final answer is recomputed from the question's own numbers by a calculator check that runs before each release; proofs and explanations were read, not machine-checked. The NCERT textbook is the authority — if something here disagrees with it, follow the book.
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In-text (page 158) Q1
Define 1 dioptre of power of a lens.
- The power of a lens is defined as the reciprocal of its focal length.
why?
Power of a lens P = 1/f with f in metres; the unit is the dioptre (D). A convex lens has positive power and a concave lens negative.
- The SI unit of focal length is the metre (m).
- Therefore, the SI unit of power is the reciprocal of the metre, which is m⁻¹.
- One dioptre is the power of a lens whose focal length is 1 metre.
why?
Power of a lens P = 1/f with f in metres; the unit is the dioptre (D). A convex lens has positive power and a concave lens negative.
- Mathematically, 1 dioptre = 1 m⁻¹.
why?
Power of a lens P = 1/f with f in metres; the unit is the dioptre (D). A convex lens has positive power and a concave lens negative.
Answer: 1 dioptre is the power of a lens of focal length 1 metre.
- The power of a lens is defined as the reciprocal of its focal length.
In-text (page 158) Q2
A convex lens forms a real, inverted image of a needle 50 cm away, the same size as the needle. Where is the needle, and what is the power of the lens?
- Given: image distance v = 50 cm, magnification m = -1 (real and inverted, same size).
why?
Magnification m = height of image ÷ height of object (= −v/u for a mirror, v/u for a lens). A negative m means a real, inverted image; a positive m a virtual, erect one.
- Using magnification formula m = v/u, we get -1 = 50/u, so u = -50 cm.
why?
Magnification m = height of image ÷ height of object (= −v/u for a mirror, v/u for a lens). A negative m means a real, inverted image; a positive m a virtual, erect one.
- The needle is placed 50 cm in front of the lens.
- Using lens formula 1/f = 1/v - 1/u, we get 1/f = 1/50 - 1/(-50) = 2/50 = 1/25.
why?
Lens formula 1/v − 1/u = 1/f, with distances measured from the optical centre using the New Cartesian sign convention.
- So focal length f = 25 cm = 0.25 m.
- Power P = 1/f (in metres) = 1/0.25 = 4 D.
why?
Power of a lens P = 1/f with f in metres; the unit is the dioptre (D). A convex lens has positive power and a concave lens negative.
- Since the lens is convex, the power is positive, so P = +4 D.
Answer: The needle is 50 cm from the lens and the power of the lens is P = +4 D
- Given: image distance v = 50 cm, magnification m = -1 (real and inverted, same size).
In-text (page 158) Q3
Find the power of a concave lens of focal length 2 m.
- The focal length of the concave lens is given as 2 m.
- According to the sign convention, the focal length of a concave lens is negative, so f = −2 m.
- The formula for the power of a lens is P = 1/f, where f is in metres.
why?
Power of a lens P = 1/f with f in metres; the unit is the dioptre (D). A convex lens has positive power and a concave lens negative.
- Substituting the value, P = 1/(−2).
- Calculating the result gives P = −0.5 D.
Answer: P = -0.5 D
Other exercises in this chapter
- In-text questions (page 142) — 4 questions
- In-text questions (page 145) — 2 questions
- In-text questions (page 150) — 5 questions
- End-of-chapter exercises — 17 questions
← Light – Reflection and Refraction: notes, practice and all exercises
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