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These are complete NCERT Solutions for CBSE Class 10 Science Chapter 10 — Light: Reflection and Refraction. For every numerical problem, the solution follows this format:
Attempt each problem yourself before reading the solution. In your board exam, every step of a numerical carries marks — always write the formula first, then substitute values with correct signs, then calculate, and finally state the answer with units and sign. Ray diagrams are described in text so you can reproduce them on paper.
Key Concepts (Quick Recap)
Reflection of Light
- Law of Reflection: (i) Angle of incidence = Angle of reflection (angle i = angle r). (ii) The incident ray, reflected ray, and normal all lie in the same plane.
- Concave mirror: Converging mirror — parallel rays converge at the focus after reflection. Reflected surface is on the inner (concave) side of the sphere.
- Convex mirror: Diverging mirror — parallel rays appear to diverge from the focus after reflection. Reflected surface is on the outer (convex) side.
- Principal focus (F): Point where parallel rays converge (concave) or appear to diverge from (convex) after reflection.
- Focal length (f): Distance from pole (P) to principal focus. f = R/2, where R = radius of curvature.
- Pole (P): Centre of the reflecting surface of the mirror.
- Centre of curvature (C): Centre of the sphere of which the mirror is a part. Distance PC = R.
Image Formation by Concave Mirror (for different object positions)
| Object Position | Image Position | Nature of Image | Size |
|---|---|---|---|
| At infinity | At F | Real, inverted | Highly diminished (point) |
| Beyond C | Between F and C | Real, inverted | Diminished |
| At C | At C | Real, inverted | Same size |
| Between C and F | Beyond C | Real, inverted | Magnified |
| At F | At infinity | Real, inverted | Highly magnified |
| Between P and F | Behind mirror | Virtual, erect | Magnified |
Image Formation by Convex Lens (for different object positions)
| Object Position | Image Position | Nature of Image | Size |
|---|---|---|---|
| At infinity | At F (other side) | Real, inverted | Highly diminished (point) |
| Beyond 2F | Between F and 2F | Real, inverted | Diminished |
| At 2F | At 2F | Real, inverted | Same size |
| Between F and 2F | Beyond 2F | Real, inverted | Magnified |
| At F | At infinity | Real, inverted | Highly magnified |
| Between F and optical centre | On same side as object | Virtual, erect | Magnified |
Mirror Formula and Sign Convention
- New Cartesian Sign Convention: All distances measured from the pole (P) of the mirror. Distances measured in the direction of incident light are positive; opposite to incident light are negative. Heights measured upward from principal axis are positive; downward are negative.
- Mirror formula: 1/v + 1/u = 1/f
- Magnification (mirror): m = -v/u = height of image / height of object = h'/h
Refraction of Light
- Refraction: Bending of light at the interface of two optically different media due to change in speed of light.
- Law of Refraction (Snell's Law): n1 sin i = n2 sin r, or sin i / sin r = n21 (refractive index of medium 2 w.r.t. medium 1).
- Refractive index: n = c/v = speed of light in vacuum / speed of light in medium. Also n = sin i / sin r.
- Light bends towards the normal when going from rarer to denser medium (speed decreases).
- Light bends away from the normal when going from denser to rarer medium (speed increases).
Lens Formula and Power
- Lens formula: 1/v - 1/u = 1/f
- Magnification (lens): m = v/u = h'/h
- Power of a lens: P = 1/f (f in metres); SI unit = dioptre (D). Convex lens: P is positive. Concave lens: P is negative.
- Convex lens (converging): f is positive; thicker at the centre; used in cameras, magnifying glasses, projectors, to correct hypermetropia.
- Concave lens (diverging): f is negative; thinner at the centre; used to correct myopia.
Intext Questions
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Ray diagram: Draw a concave mirror with P, F, C marked on the principal axis. Place the object at 10 cm from P (between P and F). Draw a ray parallel to the principal axis — it reflects through F. Draw a ray through C — it reflects back along the same path. The reflected rays actually converge at 30 cm in front of the mirror, forming a real, inverted, magnified image.
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Chapter-End Exercise
Ray diagram: Draw a concave mirror. Mark P, F, C on principal axis. Place object between P and F (close to the mirror). Draw a ray parallel to the principal axis — after reflection it passes through F. Draw a ray directed towards C — after reflection it retraces its path. Extend both reflected rays backward (behind the mirror) with dotted lines. They meet behind the mirror, forming a virtual, erect, magnified image.
Finding image position (v):
The positive value of v confirms the image is formed on the other side of the lens (real image).
Finding magnification and image size:
Image height h' = m x h = (-2/3) x 5 = -3.33 cm (negative means image is inverted).
Summary: The image is formed at 16.67 cm on the other side of the lens. It is real, inverted, and diminished (3.33 cm tall, smaller than the 5 cm object).
Ray diagram: Draw a convex lens with optical centre O. Mark F at 10 cm and 2F at 20 cm on both sides. Place the object (5 cm arrow upward) at 25 cm from O (beyond 2F on the left side). Draw a ray from the top of the object parallel to the principal axis — after refraction it passes through F on the right side. Draw a ray through the optical centre O — it goes straight through undeviated. The two refracted rays converge at a point between F and 2F on the right side. The image is an inverted arrow between F and 2F, smaller than the object.
Finding object distance (u):
The object is placed 30 cm in front of the lens (on the same side as the incoming light).
Ray diagram: Draw a concave lens with optical centre O. Mark F at 15 cm on both sides (virtual focus on the same side as object for a concave lens). Place the object (an upward arrow) at 30 cm from O on the left side. Draw a ray parallel to the principal axis from the top of the object — after refraction through the concave lens, it diverges as if coming from F on the left side. Draw a ray towards the optical centre O — it passes straight through. Extend the diverging refracted ray backward (dotted line) to meet the second ray. They appear to meet at 10 cm from O on the left side, forming a virtual, erect, diminished image.
Finding image position (v):
The positive value of v means the image is formed 6 cm behind the mirror (virtual image).
Finding magnification:
Summary: The image is formed 6 cm behind the convex mirror. It is virtual, erect, and diminished (smaller than the object, 0.6 times the object size).
Ray diagram: Draw a convex mirror. Mark P at the pole, F at 15 cm behind the mirror, and C at 30 cm behind the mirror on the principal axis. Place the object (an upward arrow) at 10 cm in front of the mirror. Draw a ray parallel to the principal axis — after reflection it appears to diverge from F behind the mirror. Draw a ray directed towards C behind the mirror — it reflects back along its own path. Extend both reflected rays backward behind the mirror (dotted lines). They meet at 6 cm behind P, forming a virtual, erect, diminished image.
Finding focal length:
Finding image position (v):
The positive value of v means the image is formed 8.57 cm behind the mirror (virtual image).
Finding magnification and image size:
Image height h' = m x h = (3/7) x 5 = 15/7 = 2.14 cm
Summary: The image is formed 8.57 cm behind the convex mirror. It is virtual, erect, and diminished with a height of 2.14 cm.
Ray diagram: Draw a convex mirror. Mark P, F (at 15 cm behind mirror), C (at 30 cm behind mirror). Place the object (5 cm arrow) at 20 cm in front of the mirror. Draw a ray parallel to the principal axis — after reflection it appears to diverge from F behind the mirror. Draw a ray directed towards C — it reflects back along its path. Extend both reflected rays backward behind the mirror. They meet at 8.57 cm behind P, forming a virtual, erect, diminished image of height 2.14 cm.
Finding image position (v):
The negative value of v means the image is formed 54 cm in front of the mirror (real image, on the same side as the object). The screen must be placed 54 cm from the mirror.
Finding magnification and image size:
Image height h' = m x h = (-2) x 7 = -14 cm (negative means inverted).
Summary: The screen should be placed 54 cm in front of the mirror. The image is real, inverted, and magnified with a size of 14 cm (twice the object size).
Ray diagram: Draw a concave mirror. Mark P, F at 18 cm, and C at 36 cm on the principal axis. Place the object (7 cm arrow upward) at 27 cm from P (between F and C). Draw a ray parallel to the principal axis — it reflects through F. Draw a ray through C — it reflects back along its own path. The reflected rays converge at 54 cm in front of the mirror, forming a real, inverted, magnified image of 14 cm height. Since the object is between F and C, the image forms beyond C on the same side.
Common Mistakes to Avoid
1. Wrong sign for object distance (u): The most common error is forgetting that u is always negative in the New Cartesian convention. The object is always placed in front of the mirror or on the side from which light travels, so u < 0. Always write u = -value.
2. Mixing up mirror formula and lens formula: The mirror formula is 1/v + 1/u = 1/f (plus sign between 1/v and 1/u). The lens formula is 1/v - 1/u = 1/f (minus sign between 1/v and 1/u). Writing the wrong formula is the number one cause of wrong answers.
3. Confusing magnification formulas: For mirrors, m = -v/u (negative sign is essential). For lenses, m = v/u (no negative sign). Students often forget the negative sign in the mirror magnification formula, leading to wrong image nature.
4. Wrong sign for concave mirror focal length: By New Cartesian convention, a concave mirror has negative f and negative R (the focus and centre of curvature are in front of the mirror, opposite to the direction of reflected light). Many students incorrectly write f as positive for a concave mirror.
5. Not converting cm to m for power calculation: Power P = 1/f requires f in metres. If f = 20 cm, you must convert to f = 0.20 m before calculating P. A common mistake is to use f = 20 directly, giving P = 1/20 = 0.05 D instead of the correct P = 1/0.20 = 5 D.
6. Confusing real and virtual image properties: A real image is always inverted and can be projected on a screen; a virtual image is always erect and cannot be projected. Students sometimes state a real image as erect or a virtual image as inverted, which is incorrect for single mirror/lens systems.
7. Drawing ray diagrams with incorrect ray paths: The two standard rays for mirrors are: (i) a ray parallel to the principal axis reflects through F (concave) or appears to come from F (convex), and (ii) a ray through C reflects back on itself. Students often draw rays that do not follow these rules. Always use the two standard rays.
8. Forgetting that a convex mirror always forms a virtual, diminished, erect image: Regardless of where the object is placed, a convex mirror always produces the same type of image. Students sometimes incorrectly state that a convex mirror can produce a real or magnified image.
9. Sign error with concave lens image distance: For a concave lens, the image is always on the same side as the object (virtual), so v is negative. Students sometimes assign a positive v to a concave lens image, leading to wrong answers.
10. Confusing refractive index direction: n21 means the refractive index of medium 2 with respect to medium 1 (n21 = v1/v2 = sin i / sin r). Students sometimes reverse the media, getting the reciprocal of the correct answer.
Exam Checklist
Before writing your exam, verify each item:
- [ ] I write the correct formula first (mirror: 1/v + 1/u = 1/f; lens: 1/v - 1/u = 1/f) before substituting values.
- [ ] I always assign a negative sign to the object distance u.
- [ ] I use the correct sign for f: negative for concave mirror and concave lens; positive for convex mirror and convex lens.
- [ ] I convert focal length from cm to m before calculating the power of a lens (P = 1/f in metres).
- [ ] I use m = -v/u for mirrors and m = v/u for lenses.
- [ ] I interpret the sign of magnification correctly: positive = erect, negative = inverted.
- [ ] I interpret the sign of v correctly: for mirrors, positive v = virtual (behind mirror), negative v = real (in front); for lenses, positive v = real (other side), negative v = virtual (same side as object).
- [ ] I draw ray diagrams using the two standard rays and label P, F, C clearly.
- [ ] I state the nature of the image explicitly: real/virtual, erect/inverted, magnified/diminished/same size.
- [ ] I remember that a convex mirror always forms a virtual, erect, diminished image, and a concave lens always forms a virtual, erect, diminished image.
Internal Links
- [Chapter 10 Guide — Light: Reflection and Refraction](/school/cbse/class/10/science/cbse-light-reflection-and-refraction)
- [All Class 10 Science Solutions](/school/cbse/class/10/science/solutions)
- [Class 10 Science Subject Guide](/school/cbse/class/10/science)