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Chapter 24: Problem 68

Rainbow is formed due to a combination of (a) dispersion and total internal reflection (b) refraction and absorption (c) dispersion and focussing (d) refraction and scattering

Short Answer

Expert verified
The correct answer is (a) dispersion and total internal reflection.

Step by step solution

01

Understand the Question

The question asks about the process responsible for the formation of a rainbow. We need to determine which physical phenomena contribute to rainbow formation from the given options.
02

Recall Rainbow Formation Principles

Rainbows form due to the interaction of sunlight with raindrops in the atmosphere. The primary processes involved are refraction, dispersion, and total internal reflection.
03

Eliminate Incorrect Options

Go through each option: - Option (b) refraction and absorption: Absorption is not involved in forming rainbows. - Option (c) dispersion and focussing: Focussing is not part of the rainbow formation. - Option (d) refraction and scattering: Scattering is not the right mechanism here. Only option (a) has the correct phenomena: dispersion and total internal reflection.
04

Confirm the Correct Answer

Dispersion is the process of separating light into colors, and total internal reflection occurs when light reflects internally within raindrops. Therefore, the correct combination for rainbow formation is in option (a).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Dispersion
When light, like sunlight, enters a raindrop, it undergoes a process known as dispersion. Dispersion is the phenomenon where a beam of light splits into its constituent colors. Each color corresponds to a different wavelength, and they travel at slightly different speeds when passing through a medium like water.
This speed variation causes the light to spread out into a spectrum of colors, much like a prism does.
  • Red light is bent the least. It travels the fastest and leaves the raindrop at a relatively shallow angle.
  • Violet light, on the other hand, is bent the most. It travels slower and exits the droplet at a steeper angle.
This separation of colors is what gives the rainbow its iconic multi-hued arch. The dispersion process is crucial for the vivid colors we associate with rainbows.
Total Internal Reflection
Total internal reflection occurs when light attempts to leave a medium at such a shallow angle that it reflects back inside instead of passing through. This is an essential component of rainbow formation.
Once the sunlight enters a raindrop and is dispersed, it reflects internally at an angle that exceeds the critical angle for water-air boundaries.
  • Each reflected ray contributes to the circular formation of colors that we see as a rainbow.
  • The internal reflection ensures that the light exits the raindrop again, continuing the journey of creating a visible rainbow.
This multiple internal reflection within the raindrop ensures that we see distinct bands of colors in the sky. Without this reflection, the light would simply pass through the drop, and the colors would not form a vibrant arc.
Refraction
Refraction is the bending of light as it passes from one medium to another, and it plays a significant role in the phenomenon of rainbows. Light entering a raindrop from air experiences a change in speed as it moves through water.
  • This speed shift bends the path of the light, a process known as refraction.
  • Refraction happens twice: once when the light enters the droplet and again when it exits.
The initial refraction as light enters the droplet sets the stage for its journey inside the raindrop, allowing it to undergo dispersion and internal reflections. Refracting once more as the light exits the droplet, it directs the light toward the observer鈥檚 eyes, completing the rainbow-forming process. This bending and reflection of light are what cause the rounded shape of rainbows.

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Most popular questions from this chapter

A thin plano-convex lens acts like a concave mirror of focal length \(0.2 \mathrm{~m}\), when silvered on its plane surface. The refractive index of the material of lens is \(1.5 .\) The radius of curvature of the convex surface of the lens will be (a) \(0.1 \mathrm{~m}\) (b) \(0.2 \mathrm{~m}\) (c) \(0.4 \mathrm{~m}\) (d) 08

One face \(A C\) of the glass prism is silvered as shown and the principal section of a glass prism is an isosceles triangle \(A B C\) with \(A B=A C\). The \(\Delta B A C\), if the ray incident normally on face \(A B\) and after two reflections it emerges from the base \(B C\) perpendicular to it, is (a) \(70^{\circ}\) (b) \(36^{\circ}\) (c) \(72^{\circ}\) (d) \(44^{\circ}\)

A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length \(10 \mathrm{~cm}\). The diameter of the sun is \(1.39 \times 10^{9} \mathrm{~m}\) and its mean distance from the earth is \(1.5 \times 10^{11} \mathrm{~m}\). What is the diameter of the sun's image on the paper? (a) \(6.5 \times 10^{-5} \mathrm{~m}\) (b) \(12.4 \times 10^{-4} \mathrm{~m}\) (c) \(9.2 \times 10^{-4} \mathrm{~m}\) (d) \(6.5 \times 10^{-4} \mathrm{~m}\)

A beam of light consisting of red, green and blue colours is incident on a right-angled isosoles prism. The refractive indices of the material of the prism for the above red, green and blue wavelengths are \(1.39,1.44\) and \(1.47\) respectively. The prism will (a) separate part of the red colour from the green and blue colours (b) separate part of the blue colour form the red and green colours (c) separate all the three colours from one another (d) not separate even partially any colour from the other two colours

If an equi-convex lens of focal length \(30 \mathrm{~cm}\) is cut into two equal parts by a horizontal plane, then (a) the light transmitting area of each part becomes half of the initial (b) the intensity will reduce to half (c) the aperture becomes \(\frac{1}{\sqrt{2}}\) times of its initial value (d) all of the above
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