Refraction and refractive index, total internal reflection and the critical angle, optical fibres, and image formation by converging and diverging lenses.

What this dot point is asking

CCEA wants you to explain refraction and define refractive index, apply Snell's law, explain total internal reflection and the critical angle and their use in optical fibres, and describe image formation by converging and diverging lenses using the lens equation. Calculation questions on Snell's law, the critical angle and the lens equation appear in almost every paper.

Refraction and refractive index

Light slows when it enters an optically denser medium (larger $n$), and the wavefronts bunch together so the ray bends towards the normal. Leaving a denser medium, light speeds up and bends away from the normal. The frequency stays constant; it is the wavelength and speed that change.

Total internal reflection and optical fibres

An optical fibre has a glass core surrounded by cladding of slightly lower refractive index. Light enters one end and strikes the core-cladding boundary at angles greater than the critical angle, so it is totally internally reflected repeatedly and guided along the fibre with very little loss. This is the basis of high-speed communications and the medical endoscope, which carries an image out of the body.

Image formation by lenses

A converging (convex) lens brings parallel rays to a real focus at its focal point, a distance $f$ (the focal length) from the lens. Where the image forms depends on the object distance $u$.

For a converging lens, an object beyond the focal point gives a real, inverted image; an object inside the focal point (as in a magnifying glass) gives a virtual, upright, magnified image. A diverging (concave) lens always forms a smaller, upright, virtual image and is given a negative focal length.

Worked example: critical angle of a glass-water boundary

Examples in context

Example 1. The endoscope. A medical endoscope uses one bundle of optical fibres to carry light into the body and another to carry the reflected image out. Each fibre relies on total internal reflection at the core-cladding boundary, so light follows the bends of the fibre without escaping, letting a surgeon view internal organs through a small incision.

Example 2. A camera lens. A camera uses a converging lens to form a real, inverted image on the sensor. For a distant object ($u \rightarrow \infty$), the lens equation gives $v = f$, so the image forms one focal length behind the lens. To focus on a nearer object the lens is moved away from the sensor, increasing $v$, exactly as the lens equation predicts.

Try this

Q1. Light travels from glass of refractive index $1.5$ into air. Find the critical angle. [2 marks]

• Cue. $\sin\theta_c = \dfrac{1}{1.5} = 0.667$, so $\theta_c = 41.8^{\circ}$.

Q2. An object is placed $0.30\ \text{m}$ from a converging lens of focal length $0.20\ \text{m}$. Find the image distance. [3 marks]

• Cue. $\dfrac{1}{v} = \dfrac{1}{0.20} - \dfrac{1}{0.30} = \dfrac{1}{0.60}$, so $v = 0.60\ \text{m}$.

Q3. Calculate the power, in dioptres, of a converging lens of focal length $25\ \text{cm}$. [1 mark]

• Cue. $P = \dfrac{1}{f} = \dfrac{1}{0.25} = 4.0\ \text{D}$.