Light

Step 1: Understanding the Concept:
The nature, position, and size of an image formed by a convex lens depend on the position of the object relative to the lens.

Step 2: Detailed Explanation:
When an object is placed exactly at a distance of (twice the focal length) from the optical centre of a convex lens, the image is formed on the other side at a distance of .
This image is real, inverted, and exactly of the same size as the object.

Step 3: Final Answer:
The object must be placed at a distance twice the focal length.

Step 1: Understanding the Concept:
The human eye can focus on objects at varying distances by changing the shape of its crystalline lens.
This ability is called the accommodation of the eye.

Step 2: Detailed Explanation:
The ciliary muscles are attached to the eye lens.
When these muscles contract or relax, they change the curvature of the lens, thereby altering its focal length to focus on near or distant objects respectively.

Step 3: Final Answer:
The ciliary muscle is responsible for changing the focal length.

Step 1: Understanding the Concept:
Dentists need a magnified view of the teeth to detect cavities or other issues clearly.

Step 2: Detailed Explanation:
When an object (like a tooth) is placed close to a concave mirror (between its pole and principal focus), the mirror forms an erect, virtual, and magnified image.
This magnification helps the dentist see the tooth in greater detail.

Step 3: Final Answer:
A concave mirror is used.

Step 1: Understanding the Concept:
A convex lens is a converging lens that can form different images based on object placement.

Step 2: Detailed Explanation:
A convex lens is versatile.
For most object positions (beyond the focal point), it forms a real and inverted image on the opposite side of the lens.
This real image can be magnified, diminished, or of the same size.
However, if the object is placed very close to the lens (between the optical centre and the principal focus), it forms a virtual, erect, and magnified image on the same side as the object (like a magnifying glass).

Step 3: Final Answer:
It can form both real (inverted) and virtual (erect) images.

Step 1: Understanding the Concept:
Absolute refractive index is defined based on the speed of light.

Step 2: Detailed Explanation:
The absolute refractive index ( ) of a medium is the ratio of the speed of light in a vacuum ( ) to the speed of light in that specific medium ( ).
Mathematically, .
Saying the refractive index of water is means that light travels times faster in a vacuum than it does in water.

Step 3: Final Answer:
It means the speed of light in a vacuum is times the speed of light in water.

Step 1: Understanding the Concept:
We will use the mirror formula and linear magnification formula applying proper sign conventions.
For a concave mirror, focal length is negative. Object distance is negative.

Step 2: Key Formula or Approach:
Mirror formula:
Magnification formula:

Step 2: Detailed Explanation:
Given:
Object distance,
Focal length,
Object height,
Using the mirror formula to find image distance :
Taking LCM of 15 and 25, which is 75:
The negative sign indicates the image is formed in front of the mirror, so it is a real image.
Therefore, the screen should be placed in front of the mirror.
Now, finding magnification :
The negative magnification confirms the image is inverted.
Finding the size of the image :
The size of the image is (the negative sign indicates it is inverted).

Step 3: Final Answer:
Screen distance is , nature is real and inverted, and size is .

Step 1: Understanding the Concept:
The power of a lens is the reciprocal of its focal length expressed in meters.

Step 2: Key Formula or Approach:
Power

Step 2: Detailed Explanation:
Given Power, (Diopters).
To find focal length :
Converting to centimeters:
The positive sign of the power and focal length indicates that the lens is convex.
A convex lens converges light rays.
Therefore, it is a converging lens.

Step 3: Final Answer:
The focal length is and it is a converging lens.

Step 1: Understanding the Concept:
A rearview mirror must allow the driver to see as much of the road behind them as possible, and the images must be upright to avoid confusion.

Step 2: Detailed Explanation:
Convex mirrors are used in vehicles.
The reasons are:
1. A convex mirror always forms an erect (upright) and virtual image, regardless of the distance of the object (the vehicle behind).
2. The image formed is always diminished (smaller than the object).
Because the images are smaller, more objects can fit into the mirror's view, giving the driver a much wider field of view compared to a plane mirror.

Step 3: Final Answer:
A convex mirror is used to get a wider, erect view of traffic behind.

Step 1: Understanding the Concept:
The refractive index ( ) of a medium indicates its optical density.
A higher refractive index means light travels slower in that medium and bends more towards the normal when entering from a rarer medium (like air).

Step 2: Detailed Explanation:
The bending of light is governed by Snell's law.
For light entering from air (refractive index ) into another medium at the same angle of incidence, the angle of refraction is smaller for the medium with the higher refractive index.
Since the refractive index of glass ( ) is greater than that of water ( ), glass is optically denser than water.
Therefore, light experiences a greater change in speed and consequently bends more towards the normal in glass than in water.

Step 3: Final Answer:
Light bends more in glass because of its higher refractive index and optical density.

Step 1: Understanding the Concept:
The human eye needs to focus on objects at various distances to form a sharp image on the retina.

Step 2: Detailed Explanation:
Accommodation is the physiological process by which the vertebrate eye changes optical power to maintain a clear image or focus on an object as its distance varies.
This is achieved by the ciliary muscles changing the curvature and hence the focal length of the crystalline lens inside the eye.

Step 3: Final Answer:
It is the eye's ability to adjust its focal length to see objects at different distances clearly.

Step 1: Understanding the Concept:
If a person can see nearby objects clearly but struggles to see distant objects (like a blackboard from the back row), they suffer from near-sightedness.

Step 2: Detailed Explanation:
This defect is known scientifically as Myopia.
In a myopic eye, the image of a distant object is formed in front of the retina instead of on it, often because the eyeball is too long or the lens is too curved.
To correct this, a diverging lens is needed to spread the light rays slightly before they enter the eye, allowing the eye's lens to focus them perfectly on the retina.

Step 3: Final Answer:
The defect is Myopia, and it is corrected by wearing spectacles containing concave lenses of suitable power.

Step 1: Understanding the Concept:
A normal human eye has a near point of and a far point at infinity.

Step 2: Detailed Explanation:
The person's near point is , which is farther away than the normal .
This means he cannot see objects closer than clearly, indicating long-sightedness or Hypermetropia.
His far point is , which is much closer than infinity.
This means he cannot see objects beyond clearly, indicating short-sightedness or Myopia.
Since he exhibits symptoms of both, he is suffering from both Hypermetropia and Myopia (often associated with aging, sometimes called Presbyopia when age-related loss of accommodation is the primary cause).

Step 3: Final Answer:
The person is suffering from both Myopia and Hypermetropia.

Step 1: Understanding the Concept:
Different optical defects require different types of corrective lenses based on whether light needs to be converged or diverged before entering the eye.

Step 2: Detailed Explanation:
To correct the near point defect (Hypermetropia), converging lenses are required.
Therefore, a convex lens is used to view nearby objects (like reading).
To correct the far point defect (Myopia), diverging lenses are required.
Therefore, a concave lens is used to view distant objects.
In practice, these are usually combined into a single pair of glasses called bifocals, where the upper part contains the concave lens and the lower part contains the convex lens.

Step 3: Final Answer:
Use a convex lens for near vision and a concave lens for distant vision.

Step 1: Understanding the Concept:
When sunlight passes through the Earth's atmosphere, it interacts with gases and particles, causing scattering of light.

Step 2: Detailed Explanation:
Sunlight is composed of various colors (the visible spectrum).
According to Rayleigh scattering, the amount of scattering is inversely proportional to the fourth power of the wavelength ( ).
Blue light has a shorter wavelength compared to red light.
Therefore, the fine particles and molecules (like nitrogen and oxygen) in the atmosphere scatter the blue light in all directions much more strongly than they scatter the longer wavelengths (red/yellow).
When we look at the sky, we see this scattered blue light entering our eyes.

Step 3: Final Answer:
The sky is blue because atmospheric molecules scatter shorter-wavelength blue light more efficiently than other colors.

Step 1: Understanding the Concept:
For spherical mirrors with small apertures, there is a direct mathematical relationship between the radius of curvature and the focal length.

Step 2: Key Formula or Approach:
Focal length ( ) =

Step 2: Detailed Explanation:
Given:
Radius of curvature, .
Using the formula:

Step 3: Final Answer:
The focal length of the mirror is .