CDS Physics · Light and Optics

Reflection and Mirrors

Light travelling in straight lines and the shadows it makes, the laws of reflection and the plane mirror, and how concave and convex mirrors form images.

All Light and Optics notes

Why this matters

Nine CDS questions from 2016 (II) to 2026 (I). Two are about straight-line travel and shadows, three about the plane mirror, and four about curved mirrors, two of them short sums with the mirror formula.

Concept 1 of 3: Light travels in straight lines: shadows

In a medium that is the same all the way through, light goes in a straight line. That is why an opaque object casts a shadow: light cannot bend round it. If the light comes from a single point, the edge of the shadow is sharp. If it comes from a broad source, like a large lamp, some parts near the edge get light from part of the source, and the edge looks blurred.

Definition

Straight-line travel and shadows:

Rectilinear propagation: light travels in straight lines in a homogeneous (uniform) transparent medium. Where the refractive index changes, the path bends.
Umbra: the fully dark part of a shadow, which gets no light from the source.
Penumbra: the partly lit fringe round the umbra, made when the source is extended (has size).
A point source gives only an umbra, so its shadow has a sharp edge. The shadow is seen on an opaque screen.
A pinhole camera forms an inverted image because rays from the top and bottom of the object cross at the pinhole.
In a solar eclipse, places in the Moon's umbra see a total eclipse and places in its penumbra a partial one.

Situation	What you see
Light in a uniform transparent medium	A straight pathQ CDS 2016 (II): light keeps a straight line only in a homogeneous, transparent medium.
Point source and an opaque object	Umbra only: a sharp shadow
Extended source and an opaque object	Umbra with a penumbra round it: a blurred edge
Pinhole camera	Inverted real image
Standing in the Moon's umbra	Total solar eclipse

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2020 · CDS (II) 2020 — General Knowledge · Q105Moderate

Example 1 · Light and Optics · Reflection and Mirrors

Which one of the following combinations of source and screen would produce sharpest shadow of an opaque object?

Straight lines need a uniform medium

Light goes straight only where the refractive index is the same everywhere. Slabs of different refractive index, or a medium whose index changes from place to place, bend the ray.

Drill 1 more on light travels in straight lines: shadows

Concept 2 of 3: Laws of reflection and the plane mirror

When light bounces off a mirror, it leaves at the same angle at which it arrived, both angles measured from the normal, the line at right angles to the mirror. A plane mirror makes an image that looks as far behind the mirror as the object is in front. No light actually goes behind the mirror, so the image cannot be caught on a screen: it is virtual.

Definition

Reflection rules:

Laws of reflection: the angle of incidence equals the angle of reflection, $i = r$ , both measured from the normal; the incident ray, the reflected ray and the normal lie in one plane.
Deviation of the ray by a plane mirror: $\delta = 180^\circ - 2i$ .
Plane mirror image: virtual, erect, the same size, laterally inverted (left and right swap), and as far behind the mirror as the object is in front.
Periscope: two plane mirrors, each at 45° to the tube, so the mirrors are parallel to each other.

Law of reflection and the deviation by a plane mirror

i = r \qquad \delta = 180^\circ - 2i

iangle of incidence, from the normal
rangle of reflection, from the normal
$\delta$ angle through which the ray is turned

Worked example

A ray strikes a plane mirror at an angle of incidence of 25°. Find the angle of reflection and the angle through which the ray is turned.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2017 · CDS (II) 2017 — General Knowledge · Q13Moderate

Example 2 · Light and Optics · Reflection and Mirrors

A ray of light is incident on a plane mirror at an angle of

40^\circ

with respect to surface normal. When it gets reflected from the mirror, it undergoes a deviation of

Angles are measured from the normal

If a stem gives the angle with the mirror surface, subtract it from 90° first. A ray at 30° to the surface has

i = 60^\circ

, and its deviation is 60°, not 120°.

A plane mirror's image is virtual

The image is erect, the same size and laterally inverted, but it is never real: the rays only seem to come from behind the mirror.

Drill 2 more on laws of reflection and the plane mirror

Concept 3 of 3: Concave and convex mirrors

A concave mirror is curved inwards, like the inside of a bowl, and brings parallel light together at its focus. A convex mirror bulges outwards and spreads light apart, so it always shows a small, upright image of a wide view. The focus is halfway between the mirror and its centre of curvature, so the focal length is half the radius. The mirror formula then gives where any image forms.

Definition

Curved mirrors, with distances measured from the pole (New Cartesian convention: distances in front of the mirror are negative):

Focal length $f = R/2$ .
Mirror formula $\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$ ; magnification $m = -\dfrac{v}{u}$ . A negative $v$ means the image is in front of the mirror and real.
Concave mirror: object beyond C, small real image between F and C; at C, same size at C; between C and F, enlarged real image beyond C; at F, image at infinity; between F and the mirror, enlarged virtual erect image behind it.
Convex mirror: always a virtual, erect, diminished image behind the mirror, whatever the distance. Used as a rear-view mirror.
So an image that stays erect at every distance comes from a plane or a convex mirror; a concave mirror inverts it once the object is beyond F.

Focal length, mirror formula and magnification

f = \frac{R}{2} \qquad \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \qquad m = -\frac{v}{u}

Rradius of curvature
ffocal length (negative for a concave mirror)
u, vobject and image distances from the pole
mmagnification; negative means inverted

Worked example

An object stands 20 cm in front of a concave mirror of radius of curvature 30 cm. Where is the image, and what is it like?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2026 · CDS (I) 2026 — General Knowledge · Q16Moderate

Example 3 · Light and Optics · Reflection and Mirrors

An object is placed at a distance of 15 cm in front of a concave mirror with a radius of curvature of 20 cm. Which one among the following statements is correct for the image formed ?

The focus is at half the radius

For a spherical mirror

f = R/2

. An object at a distance equal to

R/2

is at the focus, so its image is at infinity, not at the centre of curvature.

Erect at every distance means plane or convex

A concave mirror gives an erect image only when the object is inside its focus. If the image stays erect wherever you stand, the mirror is plane or convex, and the stem cannot tell which.

Drill 3 more on concave and convex mirrors

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Laws of reflection and the plane mirror
Law of reflection and the deviation by a plane mirror
$i = r \qquad \delta = 180^\circ - 2i$
Concave and convex mirrors
Focal length, mirror formula and magnification
$f = \frac{R}{2} \qquad \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \qquad m = -\frac{v}{u}$

Reference tables (1)

Light travels in straight lines: shadows5 rows

Situation	What you see
Light in a uniform transparent medium	A straight pathQ CDS 2016 (II): light keeps a straight line only in a homogeneous, transparent medium.
Point source and an opaque object	Umbra only: a sharp shadow
Extended source and an opaque object	Umbra with a penumbra round it: a blurred edge
Pinhole camera	Inverted real image
Standing in the Moon's umbra	Total solar eclipse

Watch out for (5)

Straight lines need a uniform medium
→ Light travels in straight lines: shadows
Angles are measured from the normal
→ Laws of reflection and the plane mirror
A plane mirror's image is virtual
→ Laws of reflection and the plane mirror
The focus is at half the radius
→ Concave and convex mirrors
Erect at every distance means plane or convex
→ Concave and convex mirrors

Test yourself on Light and Optics

15 past CDS questions from this chapter, timed at 15 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

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