Light is a form of electromagnetic radiation that travels in straight lines at approximately 3 x 108 m/s in vacuum. This chapter covers how light behaves when it strikes surfaces (reflection) and when it passes from one medium to another (refraction).
Reflection of Light
- 1.Laws of Reflection:
- 2.The angle of incidence (i) equals the angle of reflection (r): i = r.
- 3.The incident ray, reflected ray, and normal all lie in the same plane.
- Spherical Mirrors are curved mirrors that are part of a hollow sphere.
- Concave mirror: Reflecting surface curves inward (like a cave). Used in torches, car headlights, shaving mirrors.
- Convex mirror: Reflecting surface curves outward. Used as rear-view mirrors in vehicles.
- Important terms:
- Centre of curvature (C): Centre of the sphere of which the mirror is a part.
- Pole (P): Midpoint of the mirror surface.
- Principal focus (F): Point where rays parallel to the principal axis converge (concave) or appear to diverge from (convex) after reflection.
- Radius of curvature (R): Distance from pole to centre of curvature.
- Focal length (f): f = R/2.
Mirror Formula: 1/v + 1/u = 1/f
where v = image distance, u = object distance, f = focal length.
Magnification: m = -v/u = hi / ho
(negative m means inverted image; positive m means erect image)
Sign Convention (New Cartesian): Distances measured from pole (P). Distances in the direction of incident light are positive; opposite direction are negative.
Refraction of Light
Refraction: Bending of light as it passes from one transparent medium to another due to change in speed.
- 1.Laws of Refraction (Snell's Law):
- 2.The incident ray, refracted ray, and normal at the point of incidence all lie in the same plane.
- 3.n1 sin(i) = n2 sin(r) (Snell's Law)
Refractive index (n): n = speed of light in vacuum / speed of light in medium = c/v.
Relative refractive index: n21 = n2/n1 = sin(i)/sin(r)
- Lenses are transparent objects that refract light.
- Convex (converging) lens: Thicker at centre; converges light. Used in magnifying glasses, cameras, human eye.
- Concave (diverging) lens: Thinner at centre; diverges light. Used for correcting myopia.
Lens Formula: 1/v - 1/u = 1/f
Power of a lens: P = 1/f (in dioptres, D), where f is in metres. Convex lens has positive power; concave lens has negative power.
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An object is placed 20 cm in front of a concave mirror of focal length 15 cm. Find the image distance.
Using 1/v + 1/u = 1/f: u = -20 cm, f = -15 cm.
1/v = 1/f - 1/u = 1/(-15) - 1/(-20) = -1/15 + 1/20 = (-4 + 3)/60 = -1/60.
So v = -60 cm. Image is 60 cm in front of the mirror (real and inverted).
A convex mirror has a radius of curvature of 30 cm. Find the focal length.
f = R/2 = 30/2 = 15 cm. Since it is a convex mirror, f = +15 cm.
An object 4 cm tall is placed 30 cm from a concave mirror of focal length 20 cm. Find magnification.
u = -30 cm, f = -20 cm. 1/v = 1/(-20) - 1/(-30) = -1/20 + 1/30 = (-3 + 2)/60 = -1/60. v = -60 cm.
m = -v/u = -(-60)/(-30) = -2. Image is twice as large and inverted. Image height = m x ho = -2 x 4 = -8 cm.
Light travels from glass (n = 1.5) to air (n = 1.0). If the angle of incidence in glass is 30 degrees, find the angle of refraction in air.
n1 sin(i) = n2 sin(r): 1.5 x sin(30) = 1.0 x sin(r). sin(r) = 1.5 x 0.5 = 0.75. r = arcsin(0.75) approximately 48.6 degrees.
A convex lens of focal length 25 cm is used as a magnifying glass. Calculate its power.
f = 25 cm = 0.25 m. P = 1/f = 1/0.25 = +4 D.
An object is placed 15 cm from a convex lens of focal length 10 cm. Find image distance.
u = -15 cm, f = +10 cm. 1/v = 1/f + 1/u = 1/10 + 1/(-15) = 1/10 - 1/15 = (3 - 2)/30 = 1/30. v = +30 cm. Image is real and on the other side.
A person uses a concave lens of focal length -50 cm. What is the power?
f = -50 cm = -0.5 m. P = 1/f = 1/(-0.5) = -2 D. Negative sign confirms it is a diverging (concave) lens.
Key Formulas
Key formulas
Common mistakes
Students often apply the mirror formula to lenses or vice versa — remember the signs differ. For mirrors: 1/v + 1/u = 1/f. For lenses: 1/v - 1/u = 1/f. Also, always apply the New Cartesian sign convention carefully — distances against the direction of incident light are negative.
Summary
Light reflects according to the equal-angles law and refracts according to Snell's Law. Spherical mirrors and lenses form images using these principles. The mirror formula, lens formula, magnification, and power of a lens are the essential mathematical tools for solving image-formation problems.