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The Human Eye and the Colourful World - Atmospheric refraction

Grade 10CBSE

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

🔑Concepts

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Atmospheric refraction is the phenomenon of bending of light as it passes through the Earth's atmosphere, which consists of layers of varying optical densities.

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The refractive index (nn) of air layers depends on their temperature and pressure. Cooler air is denser and has a higher refractive index (ncool>nhotn_{cool} > n_{hot}), causing light to bend towards the normal as it enters denser layers.

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Apparent Position of Stars: Due to atmospheric refraction, light from a star bends towards the normal as it reaches the observer. Consequently, the star appears at a position slightly higher (apparent position) than its actual position.

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Twinkling of Stars: Stars are very distant and act as point sources of light. The physical conditions of the atmosphere change continuously, causing the path of light and the apparent position of the star to fluctuate. This leads to a variation in the intensity of light reaching the eye, known as twinkling.

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

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Advanced Sunrise and Delayed Sunset: The Sun is visible to us about 22 minutes before the actual sunrise and 22 minutes after the actual sunset due to the refraction of sunlight through the atmosphere. The actual sunrise occurs when the Sun is at the horizon.

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Flattening of the Sun's Disc: At sunrise and sunset, the Sun appears flattened or oval because the lower edge of the Sun's disc is refracted more than the upper edge due to the difference in atmospheric density.

📐Formulae

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

n1sin⁡θ1=n2sin⁡θ2n_1 \sin \theta_1 = n_2 \sin \theta_2

Δttotal=Δtsunrise+Δtsunset=2 min+2 min=4 minutes\Delta t_{total} = \Delta t_{sunrise} + \Delta t_{sunset} = 2\text{ min} + 2\text{ min} = 4\text{ minutes}

💡Examples

Problem 1:

Explain why the Sun is visible to us approximately 22 minutes before the actual sunrise.

Solution:

When the Sun is slightly below the horizon, the sunlight enters the Earth's atmosphere. Since the atmosphere's density increases towards the surface, its refractive index (nn) also increases. The light rays bend towards the normal, reaching the observer's eye. For the observer, these rays appear to come from a position above the horizon. This results in an advanced sunrise.

Explanation:

This is a direct application of atmospheric refraction where light travels from an optically rarer medium (vacuum/outer space) to an optically denser medium (Earth's atmosphere).

Problem 2:

By how much is the day lengthened due to atmospheric refraction?

Solution:

Total extra time = 2 minutes (at sunrise)+2 minutes (at sunset)=4 minutes2\text{ minutes (at sunrise)} + 2\text{ minutes (at sunset)} = 4\text{ minutes}.

Explanation:

Atmospheric refraction causes the Sun to appear above the horizon even when it is actually below it at both the start and end of the day.