10 min readConcept sheetOften a 5-mark answer with two or three ray diagrams; uses come as 1-mark and 2-mark questions

Images by concave and convex mirrors: ray diagrams and uses

A concave mirror gives real, inverted images except when the object is between P and F. A convex mirror always gives virtual, erect, smaller images.

Ray parallel to the axisReflects through F (concave) or as if from F (convex)

Ray through FReflects parallel to the principal axis

Ray through CHits along the normal and returns on itself

Only erect image (concave)Object between P and F: virtual, erect, enlarged

Four rays for mirror ray diagrams (any two are enough)

Rule 1: a ray parallel to the principal axis passes through F after reflection from a concave mirror. From a convex mirror it goes outwards as if it came from F behind the mirror.
Rule 2: a ray through F (concave), or aimed towards F (convex), comes back parallel to the principal axis.
Rule 3: a ray through C (concave), or aimed towards C (convex), hits the mirror along the normal, so it returns along the same path.
Rule 4: a ray hitting the pole P at a slant reflects at the same angle on the other side of the axis.
Where two reflected rays actually meet, the image is real. Where they only seem to meet when drawn backwards as dotted lines, the image is virtual.
For every diagram: draw the principal axis and the mirror, and mark P, F and C. Draw the object as an upright arrow AB with B on the axis. Put an arrowhead on every ray.

Images formed by spherical mirrors

Object at	Image at	Size of image	Nature
Concave: infinity (very far)	F	Highly diminished, point-sized	Real and inverted
Concave: beyond C	Between F and C	Diminished	Real and inverted
Concave: at C	C	Same size	Real and inverted
Concave: between C and F	Beyond C	Enlarged	Real and inverted
Concave: at F	Infinity	Highly enlarged	Real and inverted
Concave: between P and F	Behind the mirror	Enlarged	Virtual and erect
Convex: infinity	At F, behind the mirror	Highly diminished, point-sized	Virtual and erect
Convex: between infinity and P	Between P and F, behind the mirror	Diminished	Virtual and erect

How to draw the six ray diagrams for a concave mirror

Start every diagram the same way: axis, concave mirror on the right, P on the mirror, F and C on the left (C twice as far from P as F). Draw object AB with A at the top. Draw two rays from A.

1
Object at infinity. Draw two rays parallel to the principal axis coming from the left. After reflection, draw both passing through F. They meet at F.
Image at F: point-sized, real, inverted.
2
Object beyond C. Stand AB to the left of C. From A, draw a ray parallel to the axis and reflect it through F. From A, draw a ray through F to the mirror and reflect it parallel to the axis. The rays cross below the axis between F and C: mark A′ and draw A′B′ down to the axis.
Image between F and C: smaller, real, inverted.
3
Object at C. Stand AB on C. Use the same two rays. They cross below the axis exactly at C. Draw A′B′ pointing down, as long as AB.
Image at C: same size, real, inverted.
4
Object between C and F. Stand AB between C and F. The ray parallel to the axis reflects through F. The ray from A through F reflects parallel to the axis. They cross below the axis beyond C. Draw a long A′B′ pointing down.
Image beyond C: enlarged, real, inverted.
5
Object at F. Stand AB on F. The ray parallel to the axis reflects through F. Draw a second ray from A in line with C, as if it came from C: it hits the mirror along the normal and returns on itself. The two reflected rays are parallel, so they meet only at infinity.
Image at infinity: highly enlarged, real, inverted.
6
Object between P and F. Stand AB between F and the mirror. The ray parallel to the axis reflects through F. A second ray from A in line with C returns on itself. The reflected rays spread apart. Extend both behind the mirror as dotted lines: they meet at A′. Draw A′B′ upright, larger and dotted.
Image behind the mirror: enlarged, virtual, erect.

How to draw the two ray diagrams for a convex mirror

Draw the convex mirror bulging towards the object. Mark P on it, and F and C **behind** the mirror, on the right. Every ray drawn behind the mirror is a dotted line.

1
Object at infinity. Draw two rays parallel to the axis hitting the mirror. Reflect them so they spread outwards. Extend each backwards as a dotted line: they meet at F behind the mirror.
Image at F: point-sized, virtual, erect.
2
Object anywhere in front. From A, draw a ray parallel to the axis. Reflect it outwards and dot it back to F. From A, draw a ray aimed at C: it returns on itself; dot its line to C. The two dotted lines meet at A′ between P and F. Draw A′B′ upright, small and dotted.
Image between P and F: diminished, virtual, erect.

Uses of spherical mirrors

Mirror	Use	Why it works
Concave	Torches, search-lights and vehicle headlights	A bulb at F gives a strong parallel beam
Concave	Shaving and make-up mirrors	A face between P and F gives an erect, enlarged image
Concave	Dentist's mirror	Shows a large image of the teeth
Concave	Solar furnaces and dish solar cookers	Collects sunlight at the focus to make heat
Convex	Rear-view (wing) mirrors of vehicles	Always an erect, smaller image, and a wider field of view
Convex	Round mirrors at sharp bends on hill roads	Shows a wide area of the road around the bend

In real life

The round mirrors at hairpin bends on the ghat roads to Ooty or Munnar are convex, so drivers see a wide stretch of oncoming traffic. Your scooter's side mirror is convex for the same reason.

Exam angle

1 marks: “Which mirror is used as the rear-view mirror of a vehicle, and why?” A convex mirror: it always gives an erect, diminished image and a wider field of view.

3 marks: “Draw a ray diagram to show the image formed by a concave mirror when the object is between P and F. State the nature of the image and one use of this case.” Ray parallel to the axis reflects through F; ray from the direction of C returns on itself; dotted extensions meet behind the mirror. Image virtual, erect, enlarged. Use: shaving or make-up mirror.

5 marks: “With ray diagrams, show the images formed by a concave mirror when the object is (i) beyond C, (ii) at C, (iii) between C and F. State the position, size and nature of the image in each case.” Three diagrams with two rays each. (i) Between F and C, diminished, real, inverted. (ii) At C, same size, real, inverted. (iii) Beyond C, enlarged, real, inverted.

Remember it

Concave mirror: the image stays real and upside down until the object crosses F. Inside F, it jumps behind the mirror, upright and big. Convex mirror: always small, upright and behind.