Physics · Optics · Grade 7

Car mirrors and the periscope

Why does a car in the wing mirror look farther away than it really is?

The situation

A driver looks into a mirror hundreds of times an hour: the interior rear-view mirror shows the car behind, and the side mirrors show the next lane. But why does the motorcycle in the right-hand side mirror look farther away than it really is? Why is the inside of a headlamp shaped like a silvery bowl, and why is a periscope built to see over a wall? The secret of it all is a single law — the law of reflection of light.

Topic

Reflection of light, mirrors. Car mirrors and the periscope

Key ideas

Law of reflection
Plane and spherical mirrors
Focal length

Formulas

α = β

The law of reflection: the angle of incidence equals the angle of reflection (both measured from the normal).

d^{'} = d

Plane mirror: the image is virtual, upright, the same size as the object, and as far behind the mirror as the object is in front of it.

\frac{1}{f} = \frac{1}{d} + \frac{1}{d^{'}}

The spherical mirror formula. $d^{'} < 0$ — the image is virtual (behind the mirror).

f = \frac{R}{2} (concave), f = - \frac{R}{2} (convex)

The focal length is half the radius of curvature.

Γ = \frac{| d^{'} |}{d}

Linear magnification: in a convex mirror $Γ < 1$ — the image is diminished.

Theory

Law of reflection

Geometrical optics rests on four basic laws: in a homogeneous medium light travels in a straight line (a laser beam is a straight line); crossing beams do not interfere with each other (in a corner reflector the rays cross each other); at the boundary of two media light is reflected and refracted (refraction — in the “Laser, water and optical fibre” experiment). The ray falling on a smooth surface, the normal at the point of incidence and the reflected ray lie in one plane, $α = β$ . If the mirror turns through an angle $φ$ , the reflected ray turns through $2 φ$ . Two mirrors at 90° to each other (a corner reflector) send a ray back exactly the way it came, at any angle — this is how bicycle reflectors work.

Plane mirror and periscope

The image in a plane mirror is virtual: the rays do not come from there, only the extensions of the reflected rays cross there. The image is as far behind the mirror as the object is in front of it. In a periscope two parallel mirrors are set at 45° to the horizontal: each turns the ray through 90°, and the ray comes out in its original direction but higher up.

Concave mirror: the headlamp

Rays falling on a concave mirror parallel to the axis are collected at the focus ( $F = R / 2$ ). Because rays are reversible, light from a lamp at the focus is reflected as a parallel beam — this is how headlamps and projectors work. In a spherical mirror the outer rays cross a little before the focus (spherical aberration), so headlamps are made parabolic: a parabola brings all parallel rays to a single point.

Convex mirror: a wide view

At each point of a convex mirror the normal points in a different direction, so the reflected rays spread out like a fan: the field of view is much wider than that of a plane mirror. The image is virtual, upright and diminished ( $f = - R / 2$ ). The brain takes a small image for a distant object — the motorcycle looks farther away than it really is. In the model the rays are calculated in one plane; for oblique incidence the position of the image differs slightly from the formula.

Did you know?

In 1969 the crew of Apollo 11 left a panel of corner reflectors on the surface of the Moon. A laser beam sent from the Earth hits it and returns exactly the way it came — in this way the distance to the Moon is measured to better than a centimetre.
In the USA the convex passenger-side mirror of a car must carry the warning “Objects in mirror are closer than they appear”.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

More experiments in this section

Laser, water and optical fibre — Grade 7
The eye and spectacles — Grade 7
Shadow and eclipses — Grade 7
Measuring the speed of light — Grade 9
Optical instruments — Grade 9
Interference and diffraction — Grade 11
Polarisation of light — Grade 11
Laser physics and holography — Grade 11
Luminous flux and illuminance — Grade 11
Infrared, UV and X-rays — Grade 11