Optical Instruments

Correct answer: 7–8 cm

Explanation:
The least distance of distinct vision is the minimum distance at which an object can be seen clearly without strain.

- For a normal adult, this distance is about 25 cm.
- However, children below the age of 10 generally have more flexible eye lenses, allowing them to focus on objects at a closer range.

Therefore, the least distance of distinct vision for such children is typically around 7–8 cm.

Hence, the correct answer is: 7–8 cm.

Correct answer: power of the lens

Explanation:
The dioptre (D) is the SI unit of the power of a lens. It indicates the ability of a lens to converge or diverge light.

Mathematically, power is given by: where is the focal length of the lens in centimeters.

- If is in meters, then:
- A lens with focal length of 1 meter has power of 1 dioptre.

Hence, the correct answer is: power of the lens.

Correct answer: Only (a) is true

Explanation:
Statement (a): A lens has at least one curved surface.
This is true. By definition, a lens is made from a transparent material with at least one surface that is curved (either convex or concave) to refract light.

Statement (b): A plano-concave lens has two curved surfaces.
This is false. A plano-concave lens has one flat (plano) surface and one inwardly curved (concave) surface.

Hence, only (a) is true.

A convex lens forms an image of the same size as the object when the object is placed at a distance equal to twice the focal length from the lens. This distance is known as the centre of curvature or 2F.

When the object is placed at the centre of curvature (2F), the image is:

• Real
• Inverted
• Same size as the object
• Formed at the centre of curvature on the other side of the lens

Answer: at the centre of curvature

A lens is an optical device made from transparent material with at least one curved surface that refracts light. The deviation of light by a lens depends on the path it takes relative to its optical properties. Let's analyze the options:

1. Ray passing along the principal axis: A ray traveling along the principal axis, which is the straight line passing through the optical center and is perpendicular to the lens surfaces, does not deviate as both surfaces are perpendicular to this path.
2. Ray passing through the optic center: A ray passing through the optic center of the lens continues in the same direction, without deviation, because the lens surfaces are parallel at this point, hence no angular refraction occurs.
3. Ray passing parallel to the principal axis: A ray parallel to the principal axis will deviate after refraction. In a converging lens (convex), this ray will refract towards the focal point on the opposite side of the lens. Thus, it undergoes deviation.
4. None of the above: This option does not apply, as we have identified cases (option 3) where deviation definitely occurs.

Based on our analysis, the correct answer is: Ray passing parallel to the principal axis. This ray undergoes deviation as it refracts due to the lens's curvature, focusing at the focal point.

To understand why a concave lens always forms a certain type of image irrespective of the object's position, let's explore how concave lenses work. A concave lens, also known as a diverging lens, has a surface that curves inward. This shape causes light rays that pass through the lens to spread out or diverge. When parallel light rays (coming from an object) strike a concave lens, they refract and diverge away from the principal axis.

To analyze the image formation, we utilize ray diagrams:

• Ray 1: A ray parallel to the principal axis refracts through the lens and appears to diverge from the focal point on the same side.
• Ray 2: A ray passing through the optical center of the lens goes undeviated.

These rays never actually meet on the opposite side of the lens. Instead, they appear to originate from a point on the same side as the object. Consequently, the image is formed where the rays appear to diverge, meaning:

• Nature of Image: The image formed is virtual because it cannot be projected on a screen.
• Orientation of Image: The image is erect as it preserves the orientation of the object.

Therefore, irrespective of the object's position on the principal axis, a concave lens always forms an image that is virtual and erect.

When doctors test for defects of vision such as myopia (short-sightedness) or hypermetropia (long-sightedness), they prescribe corrective lenses based on their power.

The power of a lens is a measure of its ability to converge or diverge light rays and is given by the formula:

Where:

• is the power in diopters (D)
• is the focal length in centimeters

Doctors write prescriptions using the unit diopter (D), which directly corresponds to the power of the lens required to correct the vision.

Final Answer: power

The blue colour of the sky is primarily due to a phenomenon known as Rayleigh scattering, which occurs when sunlight interacts with the molecules in the atmosphere. This scattering is significantly influenced by the presence of gases such as nitrogen ( ) and oxygen ( ).

Sunlight is composed of a spectrum of colours, each with different wavelengths. Blue light has a shorter wavelength compared to other visible colours, such as red or yellow. According to Rayleigh's scattering law, the amount of scattering is inversely proportional to the fourth power of the wavelength. This means that shorter wavelengths are scattered more than longer wavelengths.

The small molecules of and in the atmosphere scatter the shorter blue wavelengths of sunlight in all directions, making the sky appear blue from every direction we look.

In conclusion, the blue colour of the sky is due to the scattering of light primarily by the molecules of nitrogen ( ) and oxygen ( ).

In optics, when light passes through a prism and is refracted, it undergoes deviation. A special scenario occurs at the angle of minimum deviation, where the incident ray, refracted ray inside the prism, and the emergent ray are symmetrically disposed with respect to the surfaces of the prism.

At the angle of minimum deviation, a key characteristic is that the angle of incidence and the angle of emergence are equal. This symmetry simplifies the path of light through the prism, resulting in the minimum possible deviation of the light ray.

Mathematically, this can be represented as:

This equality arises because the light traverses the prism path symmetrically: the path inside the prism and the points of entering and exiting the medium are at equal angles.

Thus, the correct statement is: