Mirrors and lenses
Drag the object. Watch the rays.
Mirrors and lenses
Drag the object or type values. Signs follow the New Cartesian convention: distances are measured from the pole or optical centre, along the incident light is positive, against it negative, and heights above the axis are positive. So u is negative for a real object.
Concave mirror of focal length -10 cm. An object +2 cm tall at u = -15 cm: the image is at v = -30 cm, real, inverted, enlarged.
Show the working
- f = R/2 = -20/2 = -10 cm, u = -15 cm (the object is in front, so u is negative), h = +2 cm.
- 1/v = 1/f - 1/u = 1/(-10) - 1/(-15) = -5/150 = -1/30
- v = -30 cm: negative, so the image is in front of the mirror and real.
- m = -v/u = -(-30)/(-15) = -2: negative, so inverted, and enlarged.
- h′ = m × h = -2 × +2 = -4 cm
Refraction
Snell's law: n₁ sin i = n₂ sin r, so sin i / sin r = n₂₁ = n₂/n₁. Angles are measured from the normal. Going from a denser to a rarer medium beyond the critical angle C (sin C = n₂/n₁), there is no refracted ray. Drag the incoming ray or type an angle.
Light from n = 1 into n = 1.52 at 40° refracts at 25.02°, bending towards the normal.
Show the working
- n₁ sin i = n₂ sin r, so sin r = n₁ sin i / n₂ = 1 × sin 40° / 1.52 = 0.4229
- r = sin⁻¹(0.4229) = 25.02°
- n₂₁ = n₂/n₁ = 1.52/1 = 1.52. Light travels at c/n: 3 × 10⁸ m/s in medium 1 and 1.97 × 10⁸ m/s in medium 2.
Ray diagrams
- Concave mirror, object at infinity
- Concave mirror, object beyond C
- Concave mirror, object at C
- Concave mirror, object between C and F
- Concave mirror, object at F
- Concave mirror, object between F and P
- Convex mirror, object at infinity
- Convex mirror, object between infinity and the pole
- Convex lens, object at infinity
- Convex lens, object beyond 2F₁
- Convex lens, object at 2F₁
- Convex lens, object between 2F₁ and F₁
- Convex lens, object at F₁
- Convex lens, object between F₁ and O
- Concave lens, object at infinity
- Concave lens, object between infinity and O
All cases together
Formulas
Refraction
Same subject: dimensional formula, unit converter, significant figures, error analysis, vectors, projectile motion, atoms and quanta, circuits.
Mirrors, lenses and refraction
What is the mirror formula?
1/v + 1/u = 1/f, where u is the object distance, v the image distance and f the focal length, all measured from the pole with the New Cartesian sign convention. For a spherical mirror f = R/2.
What is the lens formula?
1/v - 1/u = 1/f, with distances measured from the optical centre. The magnification is m = h′/h = v/u, and the power is P = 1/f with f in metres, in dioptre (D).
Why is the object distance u negative?
In the New Cartesian convention the object is placed to the left, and distances measured against the direction of the incident light are negative. So a real object always has a negative u.
How do I tell a real image from a virtual one?
A real image forms where reflected or refracted rays actually meet, so it can be caught on a screen and is inverted. A virtual image forms where the rays only appear to meet when extended back, and it is erect.
Which rays are used to draw a ray diagram?
Any two of these. A ray parallel to the axis passes through the focus after reflection or refraction. A ray through the focus comes out parallel to the axis. A ray through the centre of curvature of a mirror reflects back on itself, and a ray through the optical centre of a lens goes straight on.