Refraction Of Light

To solve this problem, we need to recall the formula used for refraction at a spherical surface separating two media of different refractive indices.

1. Refraction at Spherical Surface:
When a light ray travels from a medium of refractive index to another medium with refractive index , and the interface is a curved surface of radius , the refraction formula is:

2. Meaning of Symbols:
- : object distance
- : image distance
- : radius of curvature
- : refractive index of medium where object is located
- : refractive index of the second medium

3. Evaluating the Options:

(1) – Correct ✅

(2) – Incorrect (dimensionally inconsistent)

(3) – Incorrect

(4) – Incorrect (wrong sign)

Final Answer:
The correct option is (A).

To solve the problem, we need to identify which part of the eye helps change the focal length of the eye lens.

1. Understanding the Eye's Focal Length Adjustment:
The ability of the eye lens to change its focal length, allowing it to focus on objects at different distances, is a crucial feature of vision. This adjustment is necessary for focusing on both nearby and distant objects.

2. Role of the Ciliary Muscle:
The ciliary muscles control the curvature of the eye lens, thus adjusting its focal length. When the ciliary muscles contract or relax, they change the shape of the lens, allowing the eye to focus on objects at different distances.

3. Verifying Other Options:
- The pupil controls the amount of light entering the eye, but it does not affect the focal length.
- Aqueous humour is the fluid in the anterior chamber of the eye, and it does not directly control the focal length.
- The optical nerve transmits visual information to the brain but does not control the lens' focal length.

Final Answer:
The focal length of the eye lens changes with the help of the .

To solve the problem, we need to determine what factors the focal length of a lens depends on.

1. Formula for Focal Length:
The focal length of a lens is given by the lens maker's formula:
where is the refractive index of the lens material, and and are the radii of curvature of the two spherical surfaces of the lens.

2. Analyzing the Formula:
From the lens maker's formula, we can see that the focal length depends on two factors:
- The **radius of curvature** of the lens surfaces ( and ).
- The **refractive index** ( ) of the lens material.

3. Conclusion:
Both the radius of curvature and the refractive index of the lens affect its focal length.

Final Answer:
The focal length of a lens depends on both the radius of curvature and the refractive index of the lens, which corresponds to option (C).

To solve the problem, we need to identify the defect that causes people to have difficulty seeing near objects clearly, but allows them to see distant objects clearly.

1. Understanding the Defects:
- Myopia (or nearsightedness) is a condition where people can see near objects clearly, but distant objects appear blurred. This is the opposite of the given condition.
- Cataract is a condition where the eye's lens becomes cloudy, affecting vision at all distances.
- Presbyopia is a condition associated with aging, where the ability to focus on near objects decreases, but distant vision may remain clear.
- Hypermetropia (or farsightedness) is the defect where people can see distant objects clearly, but near objects appear blurred. This matches the condition described in the question.

Final Answer:
The defect described is called Hypermetropia (Option D).

To solve the problem, we need to find the focal length of a lens when the lens power is given.

1. Understanding the Relationship Between Power and Focal Length:
The power of a lens ( ) is related to its focal length ( ) by the formula:

where is the power in diopters (D) and is the focal length in meters.

2. Given Information:
The power of the lens is given as 5D, so:

3. Finding the Focal Length:
Using the formula , we can rearrange it to find :

meters

Final Answer:
The focal length of the lens is

To solve the problem, we need to identify which molecules are responsible for the blue colour of the sky.

1. Understanding the Phenomenon:
The blue color of the sky is due to Rayleigh scattering, a phenomenon where shorter wavelengths of light (like blue and violet) are scattered more than longer wavelengths (like red). However, our eyes are more sensitive to blue light and some violet light is absorbed by the atmosphere, making the sky appear blue.

2. Role of Atmospheric Molecules:
The primary gases in the Earth's atmosphere that cause this scattering are nitrogen (N₂) and oxygen (O₂). These molecules are small enough to scatter shorter wavelengths effectively.

Final Answer:
The correct molecules responsible for the blue color of the sky are .

To solve the problem, we need to calculate the focal length of a double concave lens placed in air using the lens maker’s formula. The radii of curvature are given as and , and the refractive index .

1. Lens Maker’s Formula:
The lens maker’s formula for a lens in air is:

2. Sign Convention:
For a double concave lens:
- The first surface is convex from the side of the incident light, so
- The second surface is concave from the side of the incident light, so
(Note: R₁ is negative and R₂ is positive for a double concave lens)

3. Substituting Values:

4. Final Calculation:

Final Answer:
The focal length of the lens is .

To solve the problem, we need to analyze the behavior of refracted rays from a convex lens when they travel parallel to the principal axis.

1. Understanding the Ray Behavior:
In the case of a convex lens, rays of light that are incident parallel to the principal axis converge at the focal point on the opposite side of the lens.
However, in this question, it is stated that the **refracted rays themselves** are travelling parallel to the principal axis.

2. Interpreting the Ray Direction:
If the refracted rays are parallel to the principal axis, then it means the object was placed at the **focus** of the lens.\\ This is because when light rays pass through a convex lens from the focal point, they emerge parallel to the principal axis.

3. Resulting Image Formation:
When refracted rays are parallel, they never meet — not even at infinity — thus no real image is formed.
This implies the rays appear to meet at infinity, and the image is formed at infinity.

Final Answer:
The image distance is