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Spectrum

Class 10 Physics • Chapter 06 (Deep Detail)

1. Deviation and Dispersion

Dispersion: The phenomenon of skipping of white light into its constituent colours.

Cause: Different colours have different speeds in glass (Red is fastest, Violet is slowest). Hence, they bend by different amounts.

[IMAGE PLACEHOLDER: PRISM DISPERSION]
Diagram of white light hitting a prism. Show splitting into 7 colors inside and emerging. Label Red at top and Violet at bottom of the spectrum.

Spectrum Colours (VIBGYOR):

Practice Q1: Colour Speed

CONCEPTUAL In glass, which colour travels faster: Red or Violet?

Ans: Red. ($v_{red} > v_{violet}$). This is why Red deviates less.

Practice Q2: Prism Factor

THINKING What happens to the spectrum if we use a hollow prism?

Ans: No dispersion. Light rays will emerge parallel to incident rays (like a glass slab) if faces are parallel, or just refract without splitting if filled with air. Dispersion needs a medium with varying refractive index for different colours.

Practice Q3: Dispersion Check

Q: Which colour of light travels fastest in vacuum?

Ans: All colours travel with same speed ($c$) in vacuum.

Practice Q4: Recombination
[IMAGE PLACEHOLDER: NEWTON'S COLOUR DISC / RECOMBINATION]
Two prisms inverted w.r.t to each other. White light enters first, disperses to 7 colors. 7 colors enter second inverted prism. Recombine to form white light. (Invert in dark mode).

CONCEPTUAL How can we recombine the seven colours of the spectrum to get white light back?

Ans: By placing an identical prism in an inverted position with respect to the first prism. The second prism reverses the dispersion produced by the first.

Practice Q5: Maximum Deviation

CONCEPTUAL Which colour of white light deviates the most and which deviates the least when passing through a prism? Why?

Ans: Violet deviates most (Shortest $\lambda$, slowest speed). Red deviates least (Longest $\lambda$, fastest speed).

2. Electromagnetic Spectrum

The ordered arrangement of electromagnetic waves in increasing/decreasing order of wavelength or frequency.

Properties common to all EM Waves:

Regions (Decreasing Wavelength / Increasing Frequency):

  1. Radio Waves: Radar, communications.
  2. Microwaves: Cooking, sat-com.
  3. Infrared (Heat Waves): Night vision, remote controls.
  4. Visible Light: Vision (4000 $\mathring{A}$ - 8000 $\mathring{A}$).
  5. Ultraviolet (UV): Sterilizing, Vitamin D. (Harmful to eyes).
  6. X-Rays: Fractures detection.
  7. Gamma Rays: Most penetrating, cancer treatment.
Practice Q6: Identification

BOARD CHECK Name the radiation used for: (a) Satellite Communication, (b) Sterilizing surgical instruments.

Ans: (a) Microwaves, (b) Ultraviolet rays.

Practice Q7: Wavelength Order

CONCEPTUAL Arrange X-rays, Infrared and UV rays in increasing order of frequency.

Ans: Infrared < UV < X-rays.

$$ c = \nu \lambda $$

Where $c$ = speed of light, $\nu$ (nu) = frequency, $\lambda$ (lambda) = wavelength.

Practice Q8: Calculation

NUMERICAL A radio station broadcasts at a frequency of 100 MHz. Calculate the wavelength of the radio wave.

Solution:

$f = 100 \text{ MHz} = 100 \times 10^6 \text{ Hz} = 10^8 \text{ Hz}$.

$c = 3 \times 10^8 \text{ m/s}$.

$\lambda = c / f = (3 \times 10^8) / 10^8 = 3 \text{ m}$.

Practice Q9: Wave Frequency

NUMERICAL Calculate the frequency of yellow light of wavelength 5500 $\mathring{A}$.

Solution: $\lambda = 5500 \times 10^{-10} \text{ m}$. $c = 3 \times 10^8$.

$f = c/\lambda = \frac{3 \times 10^8}{5.5 \times 10^{-7}}$

$\approx 5.45 \times 10^{14} \text{ Hz}$.

Practice Q10: Usage

IDENTIFICATION Name radiation for: (i) Photos in dark, (ii) Bone fracture.

Ans: (i) Infrared, (ii) X-rays.

3. Scattering of Light

The process of absorption and re-emission of light energy by dust particles and air molecules.

RAYLEIGH SCATTERING $$ I \propto \frac{1}{\lambda^4} $$

Violet/Blue (Shorter $\lambda$) scatters much more than Red (Longer $\lambda$).

Practice Q11: Scattering Basics

Q: Why are clouds white?

Ans: Large water droplets scatter all wavelengths equally.

Applications:

More Applications:

Practice Q12: Scatter Analysis
[IMAGE PLACEHOLDER: SCATTERING OF LIGHT]
Sunlight passing through atmosphere. Blue light scattering in all directions. Red light passing straight through to observer. (Invert in dark mode).

REASONING Why is the red light used for danger signals?

Ans: Red light has the longest wavelength in the visible spectrum. According to Rayleigh scattering ($I \propto 1/\lambda^4$), it is scattered the least by fog or smoke, allowing it to travel long distances and remain visible.

Practice Q13: Black Sky

THINKING Why does the sky appear black to an astronaut?

Ans: No atmosphere in space $\implies$ No scattering of light $\implies$ Sky appears black.