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The Human Eye and Optical Phenomena - ATMOSPHERIC REFRACTION

Grade 10CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Atmospheric Refraction: It is the phenomenon of bending of light as it passes through the Earth's atmosphere, which consists of layers of varying densities and refractive indices.

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Variation in Refractive Index: The physical conditions of the refracting medium (air) are not stationary. The density of air decreases with height, meaning the refractive index nn also decreases as altitude increases.

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Twinkling of Stars: Stars are distant point-sized sources of light. As the path of light rays from the star varies slightly due to the changing atmosphere, the apparent position of the star fluctuates and the amount of light entering the eye flickers, causing the twinkling effect.

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Apparent Position of Stars: Due to atmospheric refraction, starlight bending towards the normal as it enters denser layers makes the star appear slightly higher (above its actual position) when viewed near the horizon.

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Advanced Sunrise and Delayed Sunset: The Sun is visible to us about 22 minutes before the actual sunrise and about 22 minutes after the actual sunset because of atmospheric refraction. The total increase in day length is approximately 44 minutes.

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Flattening of the Sun's Disc: The apparent flattening of the Sun’s disc at sunrise and sunset is also due to the difference in atmospheric refraction of light from the top and bottom edges of the Sun.

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Why Planets Do Not Twinkle: Planets are much closer to Earth and are seen as 'extended sources' (a collection of many point-sized sources). The total variation in the amount of light entering our eye from all the individual point-sized sources will average out to zero, nullifying the twinkling effect.

📐Formulae

n=cvn = \frac{c}{v}

n1sin⁡θ1=n2sin⁡θ2n_{1} \sin \theta_{1} = n_{2} \sin \theta_{2}

Total extra daylight time=Timesunrise+Timesunset\text{Total extra daylight time} = \text{Time}_{sunrise} + \text{Time}_{sunset}

💡Examples

Problem 1:

Calculate the total extra minutes of daylight provided to an observer on Earth due to atmospheric refraction during a single day.

Solution:

2 minutes (at Sunrise)+2 minutes (at Sunset)4 minutes (Total)\begin{array}{r} 2 \text{ minutes (at Sunrise)} \\ + 2 \text{ minutes (at Sunset)} \\ \hline 4 \text{ minutes (Total)} \end{array}

Explanation:

Atmospheric refraction allows us to see the Sun when it is actually below the horizon. It appears 22 minutes before it crosses the horizon in the morning and remains visible for 22 minutes after it has crossed below the horizon in the evening.

Problem 2:

Explain why the apparent position of a star is different from its actual position using the concept of refractive index nn.

Solution:

As starlight enters the Earth's atmosphere, it travels from a rarer medium (vacuum/outer space) to a denser medium (lower atmosphere). Since natmosphere>nvacuumn_{atmosphere} > n_{vacuum}, the light bends towards the normal at each layer. This continuous bending causes the light to reach the observer's eye from a higher angle, making the star appear at an apparent position S′S' which is higher than the actual position SS.

Explanation:

This is a result of light traveling through a medium with a continuously increasing refractive index nn as it approaches the Earth's surface.