When white light passes through a converging lens, different colours focus at slightly different points. This effect is called chromatic aberration. (a) Exp...

(a) Why different colours focus at different points [2]

• White light contains many different colours (wavelengths). [1]
• Each colour has a slightly different refractive index in the glass of the lens, so each is refracted by a different amount and converges at a different focal point. [1]

This is the same phenomenon (dispersion) that causes a prism to split white light into a spectrum, but here it happens within a lens.

(b) Colour that focuses closest to the lens [1]

Violet. [1]

(c) Why violet focuses closer [2]

• Violet light has a shorter wavelength and therefore a higher refractive index in glass than red light. [1]
• Because of this higher refractive index, violet is refracted more strongly by the lens, causing it to converge at a point closer to the lens. [1]

Red light, with its longer wavelength and lower refractive index, is refracted less and focuses further from the lens (F_R is further than F_V, as shown in the diagram).

(d) Problem for optical instruments [1]

The image has coloured fringes around edges, and the image is not perfectly sharp because different colours are in focus at different positions. [1]

This is especially problematic in cameras, telescopes and microscopes where image sharpness is critical.

(e) How to reduce chromatic aberration [1]

Use an achromatic doublet - a combination of a converging lens and a diverging lens made from different types of glass. [1] The two types of glass have different dispersive properties, so the diverging lens partially cancels the dispersion introduced by the converging lens without fully cancelling its focusing power.

(f) Refractive index calculation [2]

Using the formula:

\[ n = \frac{c}{v} \]

where \(c = 3.0 \times 10^8\) m/s (speed of light in air) and \(v = 1.97 \times 10^8\) m/s (speed of red light in glass):

\[ n = \frac{3.0 \times 10^8}{1.97 \times 10^8} \] [1]

\[ n = 1.52 \] [1]

This value is typical for crown glass. A refractive index greater than 1 confirms that light travels slower in glass than in air.