Revision summary

Reflection

r = i. Both angles are measured from the normal at the incidence point. An angle to the surface is complementary to an angle to the normal.

Refractive index

n = c/v: vacuum light speed divided by speed in the medium. It has no unit. Higher n means lower speed for the same light.

Refraction relationship

sin i / sin r = n₂/n₁, or n₁ sin i = n₂ sin r. For air into a material, n = sin i / sin r. Use degree-mode sine and inverse sine, not a ratio of the angles.

Focal length

f is the optical-centre-to-principal-focus distance. An axis-parallel beam identifies that focus. A distant-object image gives an approximate measurement; subtract bench readings to obtain the separation.

Follow the path before naming the result

• Higher-index entry bends an oblique transmitted ray towards the normal; lower-index entry bends it away. At normal incidence the ray is undeviated while its speed changes.
• A parallel-sided block in air gives a parallel but laterally displaced emergent ray. Draw both boundary changes.
• A plane-mirror image is virtual, upright, the same size and equally far behind the reflecting plane, with lateral inversion. Backward extensions locate it.
• A real lens image is where actual rays meet. A virtual one is where only backward extensions meet. Both may be seen; only actual convergence forms a sharp image on a screen at that position.
• Magnified or diminished compares image height with object height. Upright or inverted compares their orientations.

Critical angle and fibres

At the critical angle, the refracted ray is at 90° to the normal. Total internal reflection requires higher-to-lower-index travel and i greater than c. Retain both medium indices when calculating the critical case. A higher-index fibre core and lower-index cladding can guide suitably incident light.

Telecommunication fibres carry high-bandwidth signals over long links with low attenuation and resistance to electromagnetic interference. Medical fibres can deliver light through a small opening; an ordered image bundle in a traditional fibrescope returns an image. Real fibres still have losses.

Lens construction reference

From the same object point, use a parallel ray refracted through the far focus and a ray through the optical centre. Find the actual or backward intersection. Beyond 2f gives a diminished real image; at 2f gives equal size; between f and 2f gives a magnified real image. These real images are inverted. Inside f gives an upright magnified virtual image. At f there is no sharp image on a screen at a finite distance.

Measure the intended angle or distance

Use a narrow ray, well-separated marks, an accurately drawn local normal and a centred protractor. Keep a glass block on its outline. Locate a plane-mirror image by backward construction or no parallax. Focus a real lens image before measuring its position and height. Distances start at the reflecting plane or optical centre, not the apparatus holder.

Repeated readings can reveal scatter, but they do not correct a wrong normal, an incorrectly placed reference or a nearby target being treated as infinitely distant.