Chapter 23, Problem 19Q

To determine

(a) To Explain:

That Light rays from stars (including our sun)always bend towards the vertical direction as they pass through the Earth’s atmosphere

Answer to Problem 19Q

Solution:

When light rays from stars (including our sun)enter from vacuum (lower refractive index medium)to our atmosphere (higher refractive index medium), then speed of light slows down and bend towards normal as per Snell's law

Explanation of Solution

The light rays, coming from the stars and sun travelling through the vacuum and enter the Earth atmosphere. The refractive index of the vacuum is lower than the refractive index of the Earth Atmosphere.

From the Snell’s law

The velocity of the light is slower and hence the refractive index of the medium is high, as given by the equation

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

Where

$n\text{ is the refractive index of the medium}$

$\text{c is the speed of light in vacuum}$

$\text{v is the speed of light in atmosphere}\text{.}$

Also from the equation,

$\frac{n_1}{n_2}=\frac{\sin {\theta }_i}{\sin {\theta }_r}$

Where

${\theta }_i\text{ is the angle of incidence}$

${\theta }_r\text{is the angle of incidence}$

$n_2\text{ the refractive index of the vacuum}$

${\text{n}}_1\text{ the refractive index of the atmosphere}$

At the boundary of the Earth atmosphere, as the light rays enter the Earth atmosphere of high refractive index, the angle of refraction is low and so the rays are bent toward the normal and the refracted rays are only observed by the observers at Earth.

To determine

(b) To determine:

The apparent positions of stars as viewed from Earth if Light rays from stars (including our sun)always bend toward the vertical direction as they pass through the Earth’s atmosphere

Answer to Problem 19Q

Solution:

When light rays enter from vacuum (lower refractive index medium)to our atmosphere (higher refractive index medium), as per Snell's law the light rays are bent towards the vertical direction.

As the observers sitting on Earth can see the refracted light rays, they interpret that they are seeing the image of the Sun and the stars appear to come from the apparent position as depicted by the figure.

As light rays come from very far away distance and the distances of the objects are too high, the apparent position of the Sun and stars cannot be practically predicted.

Explanation of Solution

The Sun and the stars that are viewed by the observers on Earth are the apparent position of the Sun and the stars. Because, the observer can see the refracted light rays from the Sun and the Star

As the light rays are come from the vacuum and enters the air atmosphere and it undergo refraction at the boundary of the earth atmosphere.

These refracted rays are viewed by the earth observer and hence they are viewing the image of the Sun and the stars, which are the apparent position.

The situation is depicted by the figure below.

But, the apparent location of the Sun and star, cannot determined as the object are situated at very far distance, the observe cannot predict that the position of the Sun and the star, whether it is above or below or sideways of the real objects, that the position with respect to the real object is beyond the knowledge of the observer.