Lesson 11: Reflection of Light

In the figure : In the figure a plane mirror gives a virtual image as far behind the mirror as the object is in front.

Rule 1: Reflection and mirrors — Light is electromagnetic radiation which causes the sensation of vision. Smooth, flat surfaces give regular reflection, and rough surfaces reflect light irregularly. A mirror is a polished surface, and polished surfaces absorb less light. Justus von Liebig coated ordinary glass with silver to make the first silvered-glass mirror. A plane mirror is made by coating the back of flat, smooth glass with a thin film of aluminium or silver, and a coat of lead oxide protects the film and makes that side opaque.

• Easy : A polished steel plate reflects light well, while a rough stone does not.
• Medium : A road looks shiny when it is wet, because water makes the surface smoother and gives regular reflection.
• Exam-type : Why is the back of a mirror coated with a thin film of silver or aluminium? So that light is reflected strongly and nothing passes through.

Rule 2: Image in a plane mirror — Rays from a point source reflect and appear to come from a point behind the mirror. The reflected rays do not actually meet, so the image is virtual. The image is as far behind the mirror as the source is in front. An extended source gives an extended image of the same size. The image of a word is laterally inverted (left and right swapped).

• Easy : A candle 20 cm in front of a plane mirror has its image 20 cm behind it.
• Medium : You stand 3 m from a mirror. Your image is 3 m behind it, so the distance between you and your image is 3 + 3 = 6 m.
• Exam-type : You walk 1 m toward the mirror from 4 m. The distance to the mirror is now 3 m, and the distance between you and the image is 3 + 3 = 6 m, which was 8 m. So it changes by 2 m for every 1 m you move.

Spot the difference

In the figure : In the figure mirrors inclined at 90° give three images.

Rule 1: Images in inclined mirrors — For two plane mirrors inclined at angle A, n = 360° ÷ A − 1. A 90° angle gives 3 images, 60° gives 5, 120° gives 2, 45° gives 7 and 30° gives 11 images.

• Easy : At 72°: n = 360 ÷ 72 − 1 = 5 − 1 = 4 images.
• Medium : At 40°: n = 360 ÷ 40 − 1 = 9 − 1 = 8 images.
• Exam-type : To get exactly 11 images, A = 360° ÷ (11 + 1) = 360° ÷ 12 = 30°.

Rule 2: Height of the mirror — To see the full image of a person, the minimum height of the mirror must be half the height of the person. In the proof R and S are the midpoints of HE and EF, so PQ = RS = RE + ES = HE ÷ 2 + EF ÷ 2 = HF ÷ 2.

• Easy : A person 1.6 m tall needs a mirror at least 1.6 ÷ 2 = 0.8 m tall.
• Medium : A mirror 75 cm tall is enough for someone 150 cm tall: 150 ÷ 2 = 75 cm.
• Exam-type : The mirror is taller than half your height: you see the full image. If it were 60 cm for a 150 cm person, 60 is less than 75, so you would not see your full length.

Spot the difference

Rule 1: Spherical mirrors — Curved mirrors give images different from plane mirrors, as in the Laughing Chamber and in the rear view mirrors of cars. A spherical mirror is a part of a hollow glass sphere. If the inner surface reflects, it is a concave mirror; if the outer surface reflects, it is a convex mirror.

• Easy : Inside of a spoon: concave. Back of a spoon: convex.
• Medium : A car's rear view mirror is a convex mirror: it shows a wide view and a smaller image.
• Exam-type : If light falls on the inside of a curved surface of a sphere and reflects, the mirror is concave; on the outside, convex.

Rule 2: Terms related to spherical mirrors — Pole (P): centre of the mirror surface. Centre of curvature (C): centre of the sphere of which the mirror is a part. Radius of curvature (R): radius of that sphere. Principal axis: the line through the pole and the centre of curvature. Principal focus (F): the point where rays parallel to the axis meet after reflection (concave, in front of the mirror) or appear to come from (convex, behind the mirror). Focal length f: distance between the pole and the principal focus, equal to half of the radius of curvature.

• Easy : If R = 30 cm, then f = 30 ÷ 2 = 15 cm.
• Medium : If f = 8 cm, then R = 2 × 8 = 16 cm, so C is 16 cm from the pole.
• Exam-type : A concave mirror has R = 24 cm. F is 12 cm and C is 24 cm from the pole, both in front of the mirror.

Spot the difference

In the figure : In the figure a ray diagram for a concave mirror.

Rule 1: Ray rules — (1) A ray parallel to the principal axis passes through the focus after reflection. (2) A ray through the focus becomes parallel to the axis. (3) A ray through the centre of curvature returns along the same path.

• Easy : A ray parallel to the axis hits the mirror and goes through F.
• Medium : A ray going through C hits the mirror straight on and returns on the same line.
• Exam-type : Draw the image by taking two rays: one parallel to the axis through F, and one through C. Where they meet is the image of the tip.

Rule 2: Images in a concave mirror — Object between pole and focus: image behind the mirror, erect, virtual, magnified. At focus: image at infinity, inverted, real, very large. Between focus and centre of curvature: beyond C, inverted, real, magnified. At C: at C, inverted, real, same size. Beyond C: between C and F, inverted, real, diminished. At infinity: at F, inverted, real, point-sized.

• Easy : A shaving mirror is concave: your face is between P and F, so you see a magnified erect image.
• Medium : Object far beyond C gives a small, real, inverted image between C and F.
• Exam-type : Object at C (distance 2f): the image is also at C, real, inverted and the same size.

Rule 3: Convex mirror and uses — A convex mirror always gives a virtual, erect, smaller image behind the mirror, whatever the object distance. A concave mirror is a focusing mirror and a convex mirror is a dispersing mirror. Concave uses: barber and dental mirrors, shaving mirrors, torches and headlamps (a source at the focus gives a parallel beam), flood lights (source a little beyond C) and solar equipment. Convex uses: side mirrors of cars and motorcycles, and big mirrors at gates and squares.

• Easy : A convex mirror at a road corner shows traffic from a wide area.
• Medium : A torch bulb at the focus of a concave reflector sends out a parallel beam that goes far.
• Exam-type : Why is a convex mirror used as a rear view mirror? It gives an erect image and a wide field of view.

Spot the difference

In the figure : In the figure the sign convention used in the mirror formula.

Rule 1: Cartesian sign convention — The pole is the origin and the principal axis is the X-axis. The object is placed on the left. Distances to the right and upwards are positive; distances to the left and downwards are negative. The focal length is negative for a concave mirror and positive for a convex mirror.

• Easy : An object 25 cm left of the pole: u = −25 cm.
• Medium : A concave mirror with R = 30 cm has f = −15 cm; a convex mirror with R = 30 cm has f = +15 cm.
• Exam-type : Object height is positive (above the axis). A virtual image above the axis has positive height; a real image below the axis has negative height.

Rule 2: Mirror formula and magnification — 1/v + 1/u = 1/f, valid for all spherical mirrors and all positions of the object. M = h₂ ÷ h₁ = −v ÷ u. Object height is positive; virtual image height is positive; real image height is negative; u is always negative.

• Easy : Concave, f = −12 cm, u = −36 cm: 1/v = 1/f − 1/u = −1/12 + 1/36 = −2/36, so v = −18 cm.
• Medium : M = −v ÷ u = −(−18) ÷ (−36) = −0.5. The image is real, inverted and half the size.
• Exam-type : Concave, f = −15 cm, u = −10 cm: 1/v = −1/15 + 1/10 = 1/30, so v = +30 cm and M = −30 ÷ (−10) = +3. The image is virtual, erect and three times larger.

Spot the difference