What this chapter is about
This chapter introduces how light behaves when it strikes surfaces and when it passes from one medium to another. You will learn the laws that govern reflection from mirrors and refraction through lenses, and how images are formed in each case.
Reflection from plane and spherical mirrors is studied first. You will understand how concave and convex mirrors form images and where those images appear. The mirror formula and magnification allow you to calculate image position and size.
Refraction deals with the bending of light as it enters a different medium. You will learn Snell's law, the concept of refractive index, and how convex and concave lenses form images. The lens formula and sign conventions let you solve numerical problems. After this chapter, you should be able to draw ray diagrams, apply formulas, and explain everyday phenomena like why a swimming pool looks shallower than it is.
Key ideas
- Light travels in straight lines in a uniform medium; this is called rectilinear propagation.
- The law of reflection states: the angle of incidence equals the angle of reflection, and the incident ray, reflected ray and normal all lie in the same plane.
- Spherical mirrors have a principal axis, centre of curvature (C), pole (P) and focus (F); for small apertures, the focal length f = R/2, where R is the radius of curvature.
- A concave mirror can form real, inverted images or virtual, erect images depending on the object's position; a convex mirror always forms a virtual, erect, diminished image.
- Refraction occurs because light changes speed when entering a different medium; the refractive index n = speed of light in vacuum / speed of light in the medium.
- Snell's law: n₁ sin i = n₂ sin r, where i is the angle of incidence and r is the angle of refraction.
- A convex lens converges light and can form real or virtual images; a concave lens diverges light and always forms a virtual, erect, diminished image.
- The sign convention (New Cartesian): distances measured in the direction of incident light are positive; heights above the principal axis are positive.
Formulas and facts to remember
- Mirror formula: 1/v + 1/u = 1/f, where u = object distance, v = image distance, f = focal length.
- Magnification (mirror): m = h'/h = −v/u, where h' is image height and h is object height.
- Relation between focal length and radius of curvature: f = R/2.
- Lens formula: 1/v − 1/u = 1/f.
- Magnification (lens): m = h'/h = v/u.
- Power of a lens: P = 1/f (f in metres), unit is dioptre (D).
- Refractive index of medium 2 with respect to medium 1: n₂₁ = sin i / sin r = v₁ / v₂.
- Absolute refractive index of glass ≈ 1.5; of water ≈ 1.33; of air ≈ 1.0003.
Worked examples
Example 1: Image by a concave mirror
An object 4 cm tall is placed 25 cm in front of a concave mirror of focal length 15 cm. Find the image position, nature and height.
Solution: Sign convention: u = −25 cm, f = −15 cm (concave mirror, distances on same side as object are negative).
Using mirror formula: 1/v + 1/u = 1/f 1/v + 1/(−25) = 1/(−15) 1/v = −1/15 + 1/25 = (−5 + 3)/75 = −2/75 v = −37.5 cm
The image is 37.5 cm in front of the mirror (real, on the same side as the object).
Magnification m = −v/u = −(−37.5)/(−25) = −1.5 Image height h' = m × h = −1.5 × 4 = −6 cm
The image is real, inverted and 6 cm tall.
Example 2: Refraction through a glass slab
A ray of light in air strikes a glass slab (n = 1.5) at an angle of incidence 30°. Find the angle of refraction inside the glass.
Solution: Using Snell's law: n₁ sin i = n₂ sin r 1 × sin 30° = 1.5 × sin r 0.5 = 1.5 × sin r sin r = 0.5 / 1.5 = 1/3 ≈ 0.333 r = sin⁻¹(0.333) ≈ 19.5°
The light bends towards the normal as it enters the denser medium.
Example 3: Image by a convex lens
An object is placed 30 cm from a convex lens of focal length 20 cm. Determine the image distance and magnification.
Solution: Sign convention: u = −30 cm (object on left), f = +20 cm (convex lens).
Lens formula: 1/v − 1/u = 1/f 1/v − 1/(−30) = 1/20 1/v + 1/30 = 1/20 1/v = 1/20 − 1/30 = (3 − 2)/60 = 1/60 v = +60 cm
The image forms 60 cm on the opposite side of the lens (real image).
Magnification m = v/u = 60/(−30) = −2
The image is real, inverted and twice the size of the object.
Common mistakes
- Forgetting sign conventions and putting all distances as positive → always assign signs first based on New Cartesian convention before substituting.
- Confusing focal length with radius of curvature → remember f = R/2, not f = R.
- Thinking convex mirrors can form real images → convex mirrors always form virtual, erect, diminished images.
- Using the mirror formula for a lens problem → mirror formula is 1/v + 1/u = 1/f; lens formula is 1/v − 1/u = 1/f.
- Believing light bends away from normal when entering a denser medium → light bends towards the normal when going from rarer to denser medium.
Quick revision
- Angle of incidence = angle of reflection; both rays and normal lie in one plane.
- Concave mirrors converge light; convex mirrors diverge light.
- Mirror formula: 1/v + 1/u = 1/f; lens formula: 1/v − 1/u = 1/f.
- Refractive index n = c / v; higher n means slower light and more bending.
- Power of lens in dioptres = 1 / focal length in metres.
- Use sign convention consistently: measure from the optical centre or pole along the principal axis.