Refraction Of Light

Correct answer: 30°

When a light ray travels from a rarer medium (air) to a denser medium (glass), it bends towards the normal. This means the angle of refraction is smaller than the angle of incidence.

Given: - Angle of incidence = 45°
- Glass is denser than air Therefore, the angle of refraction must be less than 45°. Among the options, only 30° satisfies this condition. So, the correct answer is 30°.

Correct answer: 1.5

The refractive index is calculated using the formula: where: - (speed of light in vacuum) - (speed of light in benzene) Hence, the correct answer is 1.5.

The phenomenon of a mirage is often encountered in physics, specifically in the study of optics and atmospheric conditions. A mirage occurs when light rays are bent due to refraction as they pass through air layers of different temperatures. This can create the illusion of water or a mirror-like surface on the road ahead, especially on hot days.
Let us examine the provided statements regarding mirages and determine which is false:

• It is an optical illusion.
• It is the real image of the sky.
• It appears on the distant road.
• It appears during hot summer day.

To solve this, we'll analyze each statement:

1. Mirages are indeed optical illusions. They are not real images, but rather optical phenomena caused by the bending of light rays.
2. The statement It is the real image of the sky is false. A mirage is not a real image; it's an illusion created by the refraction of light, making the sky appear to be reflected on the road.
3. Mirages commonly appear on distant roads due to the heat from the road surface affecting the air above it, causing the light refraction that produces the mirage effect.
4. Mirages appear during hot summer days because the temperature difference between the ground and the air causes sufficient bending of light to create the illusion.

Therefore, the statement that is false among those provided is: It is the real image of the sky.

To find the speed of light in the medium, we use the formula for the refractive index :

where is the refractive index of the medium, is the speed of light in a vacuum (approximately ), and is the speed of light in the medium.

Given that , we can rearrange the formula to solve for :

Substitute the known values into the equation:

Calculating this gives:

Therefore, the speed of light in the medium is .

Refraction is the bending of light as it passes from one medium to another with a different refractive index.
This phenomenon is governed by Snell's Law:
n₁sin(θ₁) = n₂sin(θ₂),
where n₁ and n₂ are the refractive indices of the two media, and θ₁ and θ₂ are the angles of incidence and refraction, respectively.

Refraction does not occur when the angle of incidence (θ₁) is 0º because the light ray travels perpendicular to the interface. In this case, sin(θ₁) is 0, thus according to Snell's Law, sin(θ₂) must also be 0, which means that θ₂ is 0º as well. The light continues in a straight line and does not change direction.

Therefore, refraction does not take place when the angle between the incident light ray and the normal to the interface is 0º.

Step 1: Understand the phenomenon of atmospheric refraction.
Atmospheric refraction is the bending of light caused by the varying optical density of the Earth's atmosphere. As sunlight enters the atmosphere, it passes through layers of air with gradually changing refractive indices due to variations in temperature and density.
Step 2: Explain how atmospheric refraction causes advance sunrise and delayed sunset.
When the sun is near the horizon, the sunlight has to travel through a larger portion of the atmosphere. Due to atmospheric refraction, the light rays bend as they pass through these layers. This bending causes the apparent position of the sun to be slightly higher than its actual position.

• Advance Sunrise:
  Even before the sun has actually risen above the horizon, its light rays bend due to atmospheric refraction, making it appear as if the sun has already risen. This results in an advance sunrise of about 2 minutes.
• Delayed Sunset:
  Similarly, even after the sun has actually set below the horizon, its light rays continue to bend due to atmospheric refraction, making it appear as if the sun is still visible. This causes a delayed sunset of about 2 minutes.

Step 3: Analyze the other options.

• Atmospheric scattering:
  This is the phenomenon responsible for the blue colour of the sky and the reddish appearance of the sun during sunrise and sunset. It does not directly cause the advance sunrise and delayed sunset.
• Atmospheric dispersion:
  This is the separation of white light into its constituent colours by the atmosphere, similar to how a prism works. While it occurs, it is not the primary reason for advance sunrise and delayed sunset.
• Atmospheric reflection:
  Some sunlight is reflected back into space by the atmosphere and clouds, but this does not explain the apparent shift in the sun's position near the horizon.

Therefore, advance sunrise and delayed sunset are due to atmospheric refraction.

Step 1: Recall the laws of refraction.
When a ray of light travels from one optical medium to another, it bends at the interface between the two media. This phenomenon is called refraction. The extent of bending depends on the refractive indices of the two media and the angle of incidence. Snell's law governs this bending: where and are the refractive indices of the first and second media, respectively, and and are the angles of incidence and refraction, respectively, measured with respect to the normal to the surface.
Step 2: Identify the optical densities of air and water.
Air is a rarer medium (lower optical density, refractive index ), and water is a denser medium (higher optical density, refractive index ).
Step 3: Apply Snell's law for light travelling from a rarer to a denser medium.
When light travels from a rarer medium (air) to a denser medium (water), . According to Snell's law: Since , we have . For angles between 0 and 90 degrees, a smaller sine value corresponds to a smaller angle. Therefore, .
Step 4: Interpret the change in angle with respect to the normal.
The angle of refraction is smaller than the angle of incidence . This means that the refracted ray bends towards the normal.
Step 5: Consider the case of light incident along the normal.
If the ray of light enters perpendicularly to the surface (along the normal), the angle of incidence . In this case, , and from Snell's law, , which means . So, there is no bending, and the light passes straight through. However, the question states that the light enters obliquely. Therefore, when a ray of light travels from air to water obliquely, it bends towards the normal.