Light — Reflection and Refraction
CBSE Class 10 · Science · Notes, formulas and practice questions
Revision guide for Light — Reflection and Refraction: reflection at plane and spherical mirrors, mirror formula and magnification, refraction and refractive index, lens formula, magnification and power of a lens.
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Reflection is the return of light into the same medium when it strikes a surface. A plane mirror forms an erect, virtual image that is as far behind the mirror as the object is in front. Spherical mirrors—concave and convex—can form different images depending on the position of the object, and are studied through ray diagrams using the principal axis, focus and centre of curvature. Distinguishing real images (formed by actual intersection of rays) from virtual images (formed by apparent meeting of extended rays) is fundamental for understanding the later lens work.
Quantitatively, spherical mirrors obey the mirror formula 1/f = 1/v + 1/u and magnification m = hᵢ/hₒ = −v/u, but only after a sign convention is fixed. The Cartesian sign convention measures all distances from the pole in the direction of incoming light as positive. For a concave mirror the focus is negative; for a convex mirror it is positive. Careful application of these signs tells whether an image is real (v negative for a mirror) or virtual, and how its size compares with the object.
Refraction is the bending of light that crosses a boundary between two transparent media, because its speed changes. The laws of refraction are summarised by Snell's law, n₁ sin i = n₂ sin r, and the fact that the incident, refracted and normal rays are coplanar. The refractive index n = c/v measures how far light slows down in a medium, and the optically denser medium has a larger index. These ideas explain why a ray bends towards the normal on entering glass from air and away from the normal in the reverse direction.
For lenses, the same reasoning is repeated. A convex lens converges incoming parallel rays to a real focus and has a positive focal length; a concave lens diverges them, giving a negative focal length. The lens formula 1/v − 1/u = 1/f and magnification m = hᵢ/hₒ = v/u use the same Cartesian sign convention as mirrors. Since u is measured negative for an object in front, a real image has positive v, a virtual image has negative v for a lens. Power P = 1/f quantifies how strongly a lens bends light, with sign indicating converging or diverging action.
Key terms
- Laws of reflection
- The angle of incidence (angle a ray makes with the normal) is equal to the angle of reflection, and the incident ray, reflected ray and the normal at the point of reflection all lie in the same plane.
- Plane mirror
- A plane mirror gives an image that is virtual, erect and of the same size as the object, placed as far behind the mirror as the object is in front. The image is laterally inverted.
- Spherical mirror
- A mirror shaped like a section of a sphere: concave mirrors have the reflecting surface on the inner (caved-in) side, convex mirrors on the outer (bulging) side. Their geometry is described by the pole, centre of curvature C, radius of curvature R and principal axis.
- Principal focus and focal length of a mirror
- For parallel rays travelling along the principal axis, the principal focus of a concave mirror is the point where they actually meet, and for a convex mirror it is the point from which they appear to diverge. The focal length f = R/2 is the distance of this focus from the pole, treated as negative for a concave mirror and positive for a convex mirror under the standard sign convention.
- Cartesian sign convention
- All distances are measured from the pole of the mirror (or the optical centre of a lens) along the principal axis. Distances in the direction of the incident light are positive, those in the opposite direction negative; heights above the axis are positive and those below negative.
- Mirror formula and magnification
- The mirror formula 1/f = 1/v + 1/u connects focal length, image distance and object distance. Magnification m = hᵢ/hₒ = −v/u gives how many times bigger the image is; negative m means an inverted image, positive m an erect image.
- Refraction and Snell's law
- Refraction is the bending of light when it travels at an angle from one transparent medium to another. According to Snell's law, for a given pair of media, the ratio sin i / sin r is constant; the incident ray, refracted ray and the normal lie in one plane.
- Refractive index
- The absolute refractive index of a medium is n = c/v, where c = 3 × 10⁸ m/s is the speed of light in vacuum and v its speed in the medium. A higher value means the medium is optically denser and bends light more; relative refractive index between two media is n₂₁ = n₂/n₁ = v₁/v₂.
- Lens, focal length and image formation
- A lens is a piece of transparent material having two spherical refracting surfaces. A convex lens is thicker in the middle and converges parallel rays to a real focus (f positive); a concave lens is thinner in the middle and diverges rays, with a virtual focus (f negative). The lens formula and power of a lens use distances measured from the optical centre with the same Cartesian sign convention.
Formula sheet
| What | Formula | Notes |
|---|---|---|
| Mirror focal length from radius | f = R/2 | R is the radius of curvature of a spherical mirror. f carries the same sign as R, so for a concave mirror f is negative and for a convex mirror positive. |
| Mirror formula | 1/f = 1/v + 1/u | u and v are respectively the object and image distances from the pole and f is the focal length, all measured using the Cartesian sign convention. The formula holds for paraxial rays. |
| Mirror magnification | m = hᵢ/hₒ = −v/u | hᵢ and hₒ are the heights of image and object (above or below the principal axis), while v and u are image and object distances. Negative m indicates an inverted image; positive m indicates an erect image. |
| Snell's law | n₁ sin i = n₂ sin r | i is the angle of incidence in the medium with refractive index n₁; r is the angle of refraction in the medium with refractive index n₂. Angles are measured from the normal. The formula becomes sin i / sin r = n when the first medium is air/vacuum. |
| Absolute refractive index | n = c/v | c is 3 × 10⁸ m/s, the speed of light in vacuum, and v is its speed in the medium. n is dimensionless and is always ≥ 1 for a transparent medium. |
| Lens formula | 1/v − 1/u = 1/f | u is object distance (negative if the object lies on the incident-light side), v is image distance, and f is focal length. For a convex lens f is positive; for a concave lens f is negative. |
| Lens magnification | m = hᵢ/hₒ = v/u | hᵢ and hₒ are image and object heights, and v and u are image and object distances from the optical centre. m is negative for an inverted image and positive for an erect image. |
| Power of a lens | P = 1/f | f is the focal length expressed in metres. Power P is in dioptres; 1 D = 1 m⁻¹. Convex lens gives positive power, concave lens gives negative power. |
Practice questions with answers
1. State the two laws of reflection of light.
The angle of incidence, measured from the normal, equals the angle of reflection. The incident ray, the reflected ray, and the normal to the reflecting surface at the point of incidence all lie in the same plane.
2. State the Cartesian sign convention for measuring distances in a spherical mirror.
The pole of the mirror is taken as origin. Distances measured in the direction of the incident ray are positive, and distances in the opposite direction are negative; heights above the principal axis are positive and heights below are negative.
3. A concave mirror has a focal length of 15 cm. At what distance in front of the mirror should an object be kept so that its real, inverted image is three times its size?
Take the object distance as x in front of the mirror, so u = −x. For a real inverted image three times the size, v = −3x. Using the mirror formula, 1/(−15) = 1/(−3x) + 1/(−x) = −4/(3x), which gives x = 20 cm. So the object must be placed 20 cm in front of the mirror.
4. A convex mirror has a radius of curvature of 40 cm. An object is placed 30 cm from its pole. Find the position and nature of the image.
For a convex mirror, f = R/2 = +20 cm and u = −30 cm. The mirror formula gives 1/v = 1/20 − 1/(−30) = 1/20 + 1/30 = 1/12, so v = +12 cm. The positive sign means the image is 12 cm behind the mirror, and it is virtual, erect and diminished.
5. Why does a ray of light bend towards the normal when it travels from air into glass?
As light moves from a rarer medium like air to a denser medium like glass, its speed decreases. Snell's law then requires the angle of refraction to be smaller than the angle of incidence, so the refracted ray bends towards the normal.
6. The speed of light in a transparent medium is 2 × 10⁸ m/s. Calculate the refractive index of the medium.
The absolute refractive index is n = c/v, where c = 3 × 10⁸ m/s. Substituting v = 2 × 10⁸ m/s gives n = (3 × 10⁸)/(2 × 10⁸) = 1.5.
7. A ray of light enters from air into a liquid at an angle of incidence 60° and refracts at an angle of 30°. Find the refractive index of the liquid.
Using Snell's law with air as medium 1, n = sin 60° / sin 30° = (√3/2)/(1/2) = √3. The refractive index of the liquid is √3, approximately 1.73.
8. A convex lens has focal length 20 cm. At what distance from the lens should an object be placed to obtain a real image of the same size as the object?
A real image of the same size as the object is formed when the object is at twice the focal length, i.e. at 2F. Therefore the object distance is 2 × 20 = 40 cm from the optical centre.
9. A concave lens has a focal length of 20 cm. An object is placed 30 cm from the lens. Find the position of the image and its magnification.
For a concave lens, f = −20 cm and u = −30 cm. The lens formula gives 1/v = 1/f + 1/u = −1/20 − 1/30 = −1/12, so v = −12 cm. The image is 12 cm from the lens on the same side as the object, virtual and erect; magnification m = v/u = (−12)/(−30) = 0.4.
10. The power of a convex lens is +4.0 D. Find its focal length.
Power P = 1/f, with focal length in metres. Therefore f = 1/P = 1/4 = 0.25 m = 25 cm. The focal length of the lens is 25 cm.
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