In-text Questions — Lenses and Power — Light - Reflection and Refraction

1. 11 markNCERT Cl-10 Science, In-text Qs after §9.3.8, Q1

   Define 1 dioptre of power of a lens.

   Hint. Power and focal length are reciprocals, with focal length measured in one specific unit.

   Step 1 — Recall the power formula. Power, P = 1/f, where f is measured in metres.

   Step 2 — Apply it to define 1 dioptre. Since a lens with focal length exactly 1 metre gives P = 1/1 = 1, that is why its power is called 1 dioptre.

   ✦ Answer: 1 dioptre is the power of a lens whose focal length is 1 metre (1 D = 1 m⁻¹).

   Where students slip. Defining it using focal length in centimetres — the dioptre is specifically tied to focal length in metres; using centimetres would give the wrong numeric relationship.

2. 23 marksNCERT Cl-10 Science, In-text Qs after §9.3.8, Q2

   A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the object? Also, find the power of the lens.

   Hint. A real, inverted image that's exactly the same size as the object only happens at one specific object position.

   Step 1 — Recall when a convex lens gives a same-size real image. This happens only when the object is at twice the focal length (2F), and the image also forms at 2F on the other side.

   Step 2 — Assign values. Since the image forms at 50 cm, v = +50 cm. For a same-size, inverted real image, m = −1, and since m = v/u for lenses, u = −v = −50 cm.

   Step 3 — Find the focal length. 1/v − 1/u = 1/f, so 1/50 − 1/(−50) = 1/f, giving 1/f = 1/50 + 1/50 = 1/25, so f = 25 cm = 0.25 m.

   Step 4 — Find the power. P = 1/f = 1/0.25 = +4 D.

   ✦ Answer: The needle is placed 50 cm in front of the lens, and the lens has a power of +4 D.

   Where students slip. Forgetting that 'same size and real' fixes the object at exactly 2F — without recognising this specific case, it's easy to set up the wrong pair of u and v values.

3. 32 marksNCERT Cl-10 Science, In-text Qs after §9.3.8, Q3

   Find the power of a concave lens of focal length 2 m.

   Hint. Concave lenses always carry a negative focal length by convention.

   Step 1 — Assign the sign to f. A concave (diverging) lens has a negative focal length: f = −2 m.

   Step 2 — Apply P = 1/f. P = 1/(−2) = −0.5 D.

   ✦ Answer: −0.5 D.

   Where students slip. Giving the power as +0.5 D — forgetting that a concave lens's focal length (and therefore its power) is negative by convention.

Solutions written by the tuition.in editorial team and checked against the NCERT Class 10 Science textbook, Reprint 2026-27 (jesc109.pdf) — four in-text question sets (14 questions total, not 18 as some older manifests claim) plus one end-of-chapter Exercise (17 questions, correctly counted). Total internal reflection (critical angle, optical fibres, mirage) has been removed from the current chapter.. Questions are referenced from the NCERT textbook for identification.