Rainbow Dispersion – Rankers Physics

Refraction by Spherical Surfaces: Practice Problem & Solution

Assertion (A): Rainbow is an example of the dispersion of sunlight by the water droplets. Reason (R): Light of shorter wavelength is scattered much more than light of larger wavelength.  
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Refraction by Spherical Surfaces. Understanding the underlying formula is key to arriving at the correct answer below:

Rainbows are formed due to dispersion and total internal reflection of sunlight by water droplets. Thus, (A) is true.
Rayleigh scattering states that the intensity of scattered light is inversely proportional to the fourth power of its wavelength \((I \propto 1/\lambda^4)), meaning shorter wavelengths (blue, violet) are scattered more than longer wavelengths (red). Thus, (R) is true.
However, (R) explains scattering, which is distinct from dispersion (dependence of refractive index on wavelength) responsible for the separation of colors in a rainbow. So, (R) does not explain (A).

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Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. Assertion (A): For every observer rainbow is a personal one. Reason (R): Every observer intercepts light from same water drops.  
2. Assertion (A): Law of reflection is applicable for all type of mirrors. Reason (R): Rays which are parallel to principal axis are known as paraxial rays.  
3. A glass sheet is grinded to form a double convex lens. The radius of curvature of two surfaces are 15 cm and 10 cm and the focal length of lens is 12 cm. Refractive index of glass sheet is
4. The angle of incidence for a ray of light at a refracting surface of a prism is $45^\circ$. The angle of prism is $60^\circ$. If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are: (2016 - I)
5. Assertion (A): Light of wavelength \(5500 \text  A^0\) travelling in medium 1 is incident on an interface and gets refracted into medium 2. Due to refraction, if it deviates by an angle \(15^{\circ}\), then its wavelength in medium 2 could be greater than or smaller than \(5500 \text{ A^0}\) but never the same. Reason (R): As light is refracted, its colour changes.