CIE iGCSE Co-ordinated Sciences-P3.2.4 Dispersion of light- Study Notes- New Syllabus
CIE iGCSE Co-ordinated Sciences-P3.2.4 Dispersion of light – Study Notes
CIE iGCSE Co-ordinated Sciences-P3.2.4 Dispersion of light – Study Notes -CIE iGCSE Co-ordinated Sciences – per latest Syllabus.
Key Concepts:
CIE iGCSE Co-Ordinated Sciences-Concise Summary Notes- All Topics
Dispersion of Light by a Prism
Dispersion is the phenomenon in which white light is separated into its component colours (spectrum) when it passes through a transparent medium such as a glass prism.
(b) Explanation
- White light is made up of different colours, each with a different wavelength (red has the longest, violet the shortest).
- The refractive index of glass depends slightly on wavelength — this is called material dispersion.
- Shorter wavelengths (violet, blue) are slowed down more and bend towards the normal more strongly.
- Longer wavelengths (red) are slowed less and bend less.
- As a result, when white light enters a prism, the colours spread out to form a spectrum from red to violet.
(c) Characteristics of the Spectrum
- Red light deviates the least.
- Violet light deviates the most.
- The order of colours from top to bottom: Red, Orange, Yellow, Green, Blue, Indigo, Violet (ROYGBIV).
Example
A ray of red light in air strikes a glass prism at an angle of incidence of \( 40^\circ \). The refractive index of glass for red light is \( 1.50 \). Calculate the angle of refraction inside the prism.
▶️Answer/Explanation
Step (1) – Snell’s Law:
\( n_1 \sin \theta_1 = n_2 \sin \theta_2 \)
Step (2) – Substitute values:
\( 1.00 \times \sin 40^\circ = 1.50 \times \sin \theta_2 \)
\( \sin \theta_2 = \dfrac{\sin 40^\circ}{1.50} = \dfrac{0.643}{1.50} = 0.429 \)
Step (3) – Find \( \theta_2 \):
\( \theta_2 = \sin^{-1}(0.429) \approx 25.4^\circ \)
Final Answer:
The angle of refraction for red light inside the prism is approximately \( 25.4^\circ \).
The Visible Spectrum
The visible spectrum is the portion of the electromagnetic spectrum that can be detected by the human eye. It consists of seven main colours, produced when white light is dispersed (e.g., by a prism).
(b) The Seven Colours
- Red
- Orange
- Yellow
- Green
- Blue
- Indigo
- Violet
(c) Order of Wavelength (longest to shortest)
Red → Orange → Yellow → Green → Blue → Indigo → Violet
- Red: longest wavelength (\( \approx 700~\text{nm} \))
- Violet: shortest wavelength (\( \approx 400~\text{nm} \))
(d) Order of Frequency (lowest to highest)
Violet → Indigo → Blue → Green → Yellow → Orange → Red
- Red: lowest frequency (\( f = \dfrac{c}{\lambda} \))
- Violet: highest frequency
Example
Calculate the frequency of red light of wavelength \( 700~\text{nm} \) and violet light of wavelength \( 400~\text{nm} \). Take the speed of light as \( 3.0 \times 10^8~\text{m/s} \).
▶️Answer/Explanation
Step (1) – Formula:
\( f = \dfrac{c}{\lambda} \)
Step (2) – For red light:
\( f_{\text{red}} = \dfrac{3.0 \times 10^8}{700 \times 10^{-9}} = 4.29 \times 10^{14}~\text{Hz} \)
Step (3) – For violet light:
\( f_{\text{violet}} = \dfrac{3.0 \times 10^8}{400 \times 10^{-9}} = 7.50 \times 10^{14}~\text{Hz} \)
Final Answer:
Red light frequency ≈ \( 4.3 \times 10^{14}~\text{Hz} \).
Violet light frequency ≈ \( 7.5 \times 10^{14}~\text{Hz} \).