IMAT Physics · Optics

Mirrors, Refraction and Total Internal Reflection

Light bounces off a mirror at the angle it arrived, bends towards the normal when it slows down, and is trapped inside a dense material beyond the critical angle.

All Optics notes

Why this matters

The only past question in this chapter, from 2020, asked which statements about rays and images in a concave mirror are always true. Refraction, Snell's law and total internal reflection have not been asked yet, but they are core syllabus with medical uses such as the endoscope.

Concept 1 of 4: The laws of reflection and the plane mirror image

Light hits a mirror and leaves at the same angle it arrived, like a ball bouncing without spin. Your eye traces the reflected rays straight back, so they seem to come from a point behind the glass. Nothing is really there, which is why a plane mirror image is called virtual.

Definition

Laws of reflection: the incident ray, the reflected ray and the normal (the line at right angles to the surface) lie in one plane, and the angle of incidence equals the angle of reflection.
Both angles are measured from the normal, not from the surface.
A virtual image is one the light only appears to come from; it cannot be caught on a screen. A real image is where light actually meets, and can be.

Property	Plane mirror image
Position	As far behind the mirror as the object is in front
Size	Same size as the object
Orientation	Upright, but left and right are swapped (laterally inverted)
Type	Virtual: it cannot be projected on a screen
Full-length mirror	Needs to be only half your height

Practice this conceptself-check · 4 quick reps

Angles in optics are measured from the normal

The angle of incidence is between the ray and the normal, not the surface. A ray at 30° to a mirror has an angle of incidence of 60°. The same rule applies in refraction.

Concept 2 of 4: Concave and convex mirrors: rays and images

A concave mirror curves inwards like the inside of a spoon, and it gathers rays together. A convex mirror bulges outwards and spreads rays apart, so it shows a wide view. Where the image lands, and what it looks like, depends on where the object is compared with the focal point.

Definition

The principal axis runs through the centre of the mirror. The focal point $F$ is where rays parallel to the axis meet after reflection (concave) or appear to come from (convex). The focal length is $f = R/2$ , where $R$ is the radius of curvature and $C$ the centre of curvature.
Concave mirror ray rules: a ray parallel to the axis reflects through $F$ ; a ray through $F$ reflects parallel to the axis; a ray through $C$ comes straight back. (Exact for a parabolic mirror, close for a spherical one near the axis.)
A concave mirror gives a real, inverted image when the object is beyond $F$ , and a virtual, upright, magnified image when the object is between $F$ and the mirror.
A convex mirror always gives a virtual, upright, smaller image.

Mirror and object position	Image	Use
Concave, object beyond $C$	Real, inverted, smaller, between $F$ and $C$	Telescope mirrors collecting light from far away
Concave, object at $C$	Real, inverted, same size, at $C$	Checking the radius of curvature in a lab
Concave, object between $C$ and $F$	Real, inverted, larger, beyond $C$	Projecting an enlarged image onto a screen
Concave, object at $F$	No image: the reflected rays are parallel	Torch and headlamp reflectors, with the bulb at $F$
Concave, object between $F$ and the mirror	Virtual, upright, larger, behind the mirror	Make-up and dentists' mirrors
Convex, any position	Virtual, upright, smaller, behind the mirror	Car wing mirrors and shop security mirrors

Practice this conceptself-check · 4 quick reps

A concave mirror does not always give a real, inverted image

With the object between the focal point and the mirror, a concave mirror gives a virtual, upright, magnified image. Its image is also not always larger: an object far beyond

C

gives a smaller one. Statements with "always" about concave images are usually false.

Concept 3 of 4: Refraction, refractive index and Snell's law

Light slows down in glass and water. If it hits the surface at an angle, one side of the beam slows first and the beam swings round, like a car whose wheel on one side runs onto sand. Going into a slower medium it bends towards the normal; coming out into a faster one it bends away.

Definition

The refractive index of a medium is $n = c/v$ : how many times slower light travels in it than in a vacuum. It is always at least 1 (air about 1.00, water 1.33, glass about 1.5).
Snell's law: $n_1 \sin\theta_1 = n_2 \sin\theta_2$ , with the angles measured from the normal.
Into a higher $n$ (slower): the ray bends towards the normal. Into a lower $n$ : away from it. Along the normal: no bending.
The frequency, and so the colour, stays the same; the wavelength becomes $\lambda/n$ .
$n$ is slightly different for each colour, so a prism splits white light into a spectrum (dispersion): violet bends most, red least.

Refractive index and Snell's law

n = \frac{c}{v} \qquad n_1 \sin\theta_1 = n_2 \sin\theta_2

$n$ refractive index (no unit)
$c$ speed of light in a vacuum, $3.00 \times 10^8$ m/s
$v$ speed of light in the medium
$\theta_1,\ \theta_2$ angles of incidence and refraction, from the normal

Worked example

Light in air strikes a glass block of refractive index 1.50 at an angle of incidence of 45°. Find the angle of refraction and the speed of light in the glass.

Practice this conceptself-check · 4 quick reps

Refraction changes the wavelength, not the frequency

In glass, light slows down and its wavelength shrinks by the factor

n

, but its frequency, and so its colour, is unchanged. Options claiming the colour or frequency changes inside the glass are wrong.

Concept 4 of 4: Total internal reflection and the critical angle

Light leaving glass for air bends away from the normal. Tilt the ray more and more, and the refracted ray swings down until it skims along the surface. That angle is the critical angle. Any steeper, and no light gets out at all: it is all reflected back inside. Optical fibres use this to trap light along a bent glass thread.

Definition

Total internal reflection (TIR) needs both:

light travelling from a higher to a lower refractive index (glass to air, water to air), and
an angle of incidence greater than the critical angle $C$ .
At exactly $C$ the refracted ray runs along the surface (angle of refraction 90°). From a medium of index $n$ into air, $\sin C = 1/n$ .
Uses: optical fibres for communication; the endoscope, where one bundle of fibres carries light into the body and another carries the image out; the sparkle of diamond (very small $C$ ).

Critical angle

\sin C = \frac{n_2}{n_1} \qquad \sin C = \frac{1}{n} \ \text{(into air)}

$C$ critical angle, measured from the normal
$n_1$ refractive index of the denser medium the light starts in
$n_2$ refractive index of the less dense medium

Worked example

Find the critical angle for glass of refractive index 1.50 with air outside, and with water (1.33) outside. Is a ray inside the glass meeting the surface at 45° totally reflected in each case?

Practice this conceptself-check · 4 quick reps

Total internal reflection only happens going into a less dense medium

TIR needs light travelling from a higher refractive index to a lower one, at more than the critical angle. Light entering glass from air always gets in (some is partly reflected), whatever the angle.

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)

Refraction, refractive index and Snell's law
Refractive index and Snell's law
$n = \frac{c}{v} \qquad n_1 \sin\theta_1 = n_2 \sin\theta_2$
Total internal reflection and the critical angle
Critical angle
$\sin C = \frac{n_2}{n_1} \qquad \sin C = \frac{1}{n} \ \text{(into air)}$

Reference tables (2)

The laws of reflection and the plane mirror image5 rows

Property	Plane mirror image
Position	As far behind the mirror as the object is in front
Size	Same size as the object
Orientation	Upright, but left and right are swapped (laterally inverted)
Type	Virtual: it cannot be projected on a screen
Full-length mirror	Needs to be only half your height

Concave and convex mirrors: rays and images6 rows

Mirror and object position	Image	Use
Concave, object beyond $C$	Real, inverted, smaller, between $F$ and $C$	Telescope mirrors collecting light from far away
Concave, object at $C$	Real, inverted, same size, at $C$	Checking the radius of curvature in a lab
Concave, object between $C$ and $F$	Real, inverted, larger, beyond $C$	Projecting an enlarged image onto a screen
Concave, object at $F$	No image: the reflected rays are parallel	Torch and headlamp reflectors, with the bulb at $F$
Concave, object between $F$ and the mirror	Virtual, upright, larger, behind the mirror	Make-up and dentists' mirrors
Convex, any position	Virtual, upright, smaller, behind the mirror	Car wing mirrors and shop security mirrors

Watch out for (4)

Angles in optics are measured from the normal
→ The laws of reflection and the plane mirror image
A concave mirror does not always give a real, inverted image
→ Concave and convex mirrors: rays and images
Refraction changes the wavelength, not the frequency
→ Refraction, refractive index and Snell's law
Total internal reflection only happens going into a less dense medium
→ Total internal reflection and the critical angle

Drill the past-year questions on this topic

Open the bank with this topic pre-filtered.

Open in the bank