(a) Explain the formation of a rainbow in the atmosphere after a rain shower. State the three optical phenomena involved in sequence. (b) Why does the sun appear visible to us about before the actual sunrise?
Answer
(a) A rainbow is formed due to refraction, internal reflection, and refraction again of sunlight by water droplets. (b) Atmospheric refraction bends sunlight towards the normal, making the sun appear above the horizon about before actual sunrise.
Step-by-step solution
- For part (a): Identify water droplets in the atmosphere acting as small glass prisms.
- Step 1 of rainbow formation: Incident sunlight enters a water droplet and undergoes refraction and dispersion, splitting into its component colors.
- Step 2 of rainbow formation: These light rays strike the inner surface of the droplet and undergo internal reflection.
- Step 3 of rainbow formation: The reflected light rays undergo refraction again as they exit the water droplet, reaching the observer's eye as a rainbow.
- For part (b): Explain that the Earth's atmosphere consists of layers of air with decreasing optical density from the surface upwards.
- When the sun is slightly below the horizon, light rays coming from the sun travel from optically rarer to optically denser layers of air.
- These light rays bend continuously towards the normal due to atmospheric refraction.
- As a result, the apparent position of the sun is raised slightly above the actual horizon, making the sun visible about before actual sunrise.
Common mistake: Writing total internal reflection instead of internal reflection inside the water droplet, or omitting the sequence of physical phenomena.
Concept tested: Rainbow formation and atmospheric refraction
Published · How this solution was prepared and checked
Related questions
- 1 Explain the formation of a primary and a secondary rainbow after a rain shower, mentioning the optical phenomena involved in each case.
- 2 A monochromatic red light (λ = 600 nm) and violet light (λ = 400 nm) pass through a prism whose apex angle is 30°. The refractive index of the prism for red light is 1.50 and for violet light is 1.55. Assuming small angles, calculate the angular dispersion between the red and violet rays after emerging from the prism.
- 3 Which of the following statements correctly describes the changes that occur in the eye during accommodation for a near object?
- 4 Which part of the eye contributes the greatest refractive power?
- 5 A hyperopic person can see distant objects clearly but cannot read a newspaper held at 25 cm without glasses. The far point of his eye is at infinity. Calculate the minimum power (in dioptres) of a thin converging lens that should be placed close to the eye to enable him to read at 25 cm.
- 6 A myopic person sees distant objects clearly only up to a far point of 50 cm. What is the minimum power of a lens (in dioptres) required to correct his vision so that he can see objects at infinity clearly? Assume a thin lens placed close to the eye.