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.

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.