-0.25 m. Power P = 1/f (in metres), so f = 1/P = 1/(-4) = -0.25 m.
| # | Statement (Answer in bold) |
|---|---|
| 1 | The path of the light is called as ray |
| 2 | The refractive index of a transparent medium is greater than or equal to one; for ordinary transparent media like water and glass, it is greater than one. |
| 3 | If the energy of incident beam and the scattered beam are same, then the scattering of light is called as elastic scattering. |
| 4 | According to Rayleigh's scattering law, the amount of scattering of light is inversely proportional to the fourth power of its wavelength |
| 5 | Amount of light entering into the eye is controlled by Iris |
| # | Statement | Answer | Correction (if False) |
|---|---|---|---|
| 1 | Velocity of light is greater in denser medium than in rarer medium | False | Velocity of light is lesser in denser medium than in rarer medium. |
| 2 | The power of lens depends on the focal length of the lens | True | Power of a lens is P = 1/f, where f is measured in metre. |
| 3 | Increase in the converging power of eye lens cause ‘hypermetropia’ | False | An increase in the converging power of the eye lens causes myopia, because light focuses in front of the retina. A decrease in converging power may cause hypermetropia. |
| 4 | The convex lens always gives small virtual image. | False | A concave lens always forms a virtual, erect and diminished image for a real object. A convex lens may form real or virtual images depending on object position. |
| Column A | Column B |
|---|---|
| Retina | Screen of the eye where the image is formed |
| Pupil | Opening in the iris that allows light to enter the eye |
| Ciliary muscles | Muscles that change the curvature of the eye lens for accommodation |
| Myopia | Distant objects are blurred because the image forms in front of the retina; far point comes closer; corrected by a concave lens. |
| Hypermetropia | Nearby objects are blurred because the image forms behind the retina; near point moves away; corrected by a convex lens. |
Dispersion of light is the phenomenon observed when a beam of white light passes through a transparent medium, such as a glass prism or water droplets, and splits into its constituent colours. This splitting occurs because each colour of light, corresponding to a different wavelength, travels at a slightly different speed within the medium. Consequently, each colour is refracted at a slightly different angle. Violet light, having the shortest wavelength, is deviated the most, while red light, with the longest wavelength, is deviated the least. This results in the formation of a spectrum of colours, typically observed as red, orange, yellow, green, blue, indigo, and violet (ROYGBIV).
Rayleigh's law of scattering describes how light is scattered by particles that are much smaller than the wavelength of the light, such as molecules of gas in the atmosphere. The law states that the intensity of scattered light is inversely proportional to the fourth power of its wavelength. Mathematically, this can be expressed as: Intensity of scattering ∝ 1/λ⁴, where λ is the wavelength of the light. This relationship explains why shorter wavelength colours, such as blue and violet, are scattered much more effectively by atmospheric particles than longer wavelength colours, like red and orange. This is the reason why the sky appears blue during the day, as blue light is scattered in all directions across the sky, and why sunsets and sunrises often appear red, as the blue light has been scattered away over the longer path through the atmosphere.
A convex lens is a converging lens that is thicker at the center and thinner at the edges. Its surfaces curve outwards. When parallel rays of light pass through a convex lens, they converge at a point called the principal focus, forming a real image. Consequently, a convex lens has a positive focal length. Depending on the position of the object, a convex lens can form either real, inverted images or virtual, erect, and magnified images. In contrast, a concave lens is a diverging lens that is thinner at the center and thicker at the edges, with surfaces curving inwards. When parallel rays of light strike a concave lens, they diverge as if originating from a virtual focus on the same side as the incident light. Therefore, a concave lens has a negative focal length. For a real object, a concave lens typically forms a virtual, erect, and diminished image.
A convex lens is characterized by its shape, being thicker in the middle and thinner at the edges. This specific curvature causes parallel rays of light incident upon it to converge at a point after passing through the lens. Because it brings light rays together, it is also known as a converging lens. This property makes it useful in various optical instruments where focusing light is essential.
A convex lens is termed a converging lens because of its optical behavior. When parallel rays of light strike its surface, the lens refracts these rays inwards, causing them to converge at a specific point called the principal focus. This ability to bring light rays together is the defining characteristic of a converging lens, enabling it to form real images.
A convex lens is capable of producing both real and virtual images, but it predominantly forms real images. When an object is placed at a distance greater than its focal length from the convex lens, the refracted rays converge to form a real, inverted image on the opposite side of the lens. A virtual, erect, and magnified image is formed only when the object is placed between the optical center and the principal focus of the lens.
A convex lens is effectively used to correct the vision defect known as hypermetropia, or long-sightedness. In hypermetropia, the eye's focusing power is insufficient, causing the image of nearby objects to be formed behind the retina, making them appear blurred. The convex lens, with its converging power, adds to the eye's refractive power, ensuring that light from nearby objects is focused precisely on the retina, thus restoring clear vision.
A concave lens is identified by its physical structure, which is thinner at the center and thicker at the edges. This shape causes parallel rays of light to diverge, or spread out, after refraction. Consequently, a concave lens is also referred to as a diverging lens. This divergence of light is fundamental to its optical properties and applications.
A concave lens is classified as a diverging lens because of how it interacts with light. When parallel rays of light pass through a concave lens, they are refracted outwards, spreading away from each other. These diverging rays, when traced backward, appear to originate from a point on the same side of the lens as the incident light, known as the principal focus. This spreading of light is the hallmark of a diverging lens.
A concave lens, when used with a real object, consistently produces an image that is virtual, erect, and diminished in size. This means the image cannot be projected onto a screen and appears upright and smaller than the object. The virtual nature arises because the refracted rays diverge and do not actually meet; they only appear to diverge from a point from which the image is formed.
The vision defect known as myopia, or short-sightedness, is effectively treated using a concave lens. Myopia occurs when the eye focuses distant objects in front of the retina, leading to blurred vision for faraway objects. A concave lens, being a diverging lens, reduces the converging power of the eye's optical system. It causes the incoming parallel rays from distant objects to diverge slightly before entering the eye, ensuring that the final image is formed precisely on the retina, thus correcting the defect.
Myopia, or short-sightedness, arises from two primary causes related to the eye's structure and refractive power. Firstly, the eyeball may become abnormally elongated from front to back. Secondly, the eye lens might possess excessive converging power, meaning it bends light too strongly. In either case, parallel rays from distant objects are focused at a point *in front* of the retina, rather than on it. This results in clear vision for nearby objects but blurred vision for distant ones. The condition is typically corrected by using a concave lens, which diverges the light rays before they enter the eye, effectively shifting the focal point back onto the retina.
The phenomenon responsible for the blue color of the sky is known as Rayleigh scattering. When sunlight enters the Earth's atmosphere, it collides with the tiny gas molecules present. These molecules scatter the sunlight in all directions. Blue light, having a shorter wavelength compared to other visible colors like red, is scattered much more effectively than longer wavelengths. As this scattered blue light reaches our eyes from all parts of the sky, the sky appears to be blue. This scattering is more pronounced for shorter wavelengths.
Traffic signals are designed to be red primarily because of the physics of light scattering and the psychological impact of color. Red light possesses the longest wavelength within the visible spectrum. This long wavelength means it is scattered the least by atmospheric particles like dust, water droplets, and air molecules. Consequently, red light travels longer distances without significant dispersion, making it clearly visible from afar, even in conditions of fog or haze. Furthermore, red is a color that is easily distinguishable and has been conventionally adopted as a warning or stop signal across many cultures, allowing drivers to quickly and unambiguously recognize its meaning, thus enhancing road safety.
(ii) Light travels in a straight line in a homogeneous medium.
(iii) Light can travel through vacuum and does not require a material medium.
(iv) The speed of light in vacuum is c = 3 x 10^8 m s^-1.
(v) Different colours of light have different wavelengths and frequencies.
(i) A ray parallel to the principal axis passes through the principal focus on the other side after refraction.
(ii) A ray passing through the optical centre of the lens goes undeviated.
(iii) A ray passing through the principal focus on the object side emerges parallel to the principal axis after refraction.
To obtain the image in a ray diagram, draw any two of these rays from the top of the object. The point where the refracted rays actually meet gives a real image; if the refracted rays diverge, extend them backwards to locate the virtual image. For a convex lens, the image may be real and inverted when the object is beyond F, or virtual, erect and magnified when the object is between F and the lens. Important cases are: object beyond 2F gives a diminished image between F and 2F; object at 2F gives same-size image at 2F; object between F and 2F gives a magnified image beyond 2F; object at F gives image at infinity; object within F gives a virtual, erect and enlarged image on the same side.
Myopia, commonly known as short-sightedness, is an eye defect where individuals can see nearby objects clearly but distant objects appear blurred. This occurs either because the eyeball has become too long (elongated) or because the eye lens has too much converging power. As a result, the image of distant objects is focused in front of the retina instead of on it. Myopia is corrected using a concave lens, which diverges the light rays before they enter the eye, ensuring the image is formed on the retina. Hypermetropia, or long-sightedness, is the opposite condition where nearby objects appear blurred, while distant objects are seen clearly. This defect arises when the eyeball is too short or the eye lens has insufficient converging power. Consequently, the image of nearby objects is focused behind the retina. Hypermetropia is corrected using a convex lens, which converges the light rays, helping to focus the image on the retina.
Working: The object is placed just beyond the focal length of the objective lens. The objective forms a real, inverted and magnified intermediate image inside the tube, near the focal plane of the eyepiece. This intermediate image acts as the object for the eyepiece. The eyepiece works like a simple microscope and produces a further enlarged virtual image either at the near point or at infinity. The final image is enlarged and inverted with respect to the original object.
The total magnification is the product of the magnification by the objective and the magnification by the eyepiece. For final image at the near point, approximately M = (L/f_o) x (1 + D/f_e). For final image at infinity, approximately M = (L/f_o) x (D/f_e). Here L is the tube length, f_o is the focal length of the objective, f_e is the focal length of the eyepiece and D is the least distance of distinct vision, about 25 cm.
Lens formula: 1/v - 1/u = 1/f.
1/v - 1/(-20) = 1/10
1/v + 1/20 = 1/10
1/v = 1/10 - 1/20 = 1/20, so v = +20 cm.
The positive value of v shows that the image is formed 20 cm on the right side of the lens. Magnification m = v/u = 20/(-20) = -1. Therefore, the image is real, inverted and of the same size as the object.
Lens formula: 1/v - 1/u = 1/f
=> 1/v - 1/(-10) = 1/(-15)
=> 1/v + 1/10 = -1/15
=> 1/v = -1/15 - 1/10 = - (2+3)/30 = -5/30 = -1/6
=> v = -6 cm (virtual image, 6 cm on object side).
Magnification m = v/u = (-6)/(-10) = 0.6
Image height h' = m h = 0.6 x 3 cm = 1.8 cm.
Therefore: image is virtual, erect, diminished, located 6 cm from the lens on the object side, and its size is 1.8 cm.
(b) There is no change in the focal length because the curvature of the lens surfaces does not change. However, the intensity or brightness of the image will be reduced because less light passes through the broken lens.
The eyes of nocturnal birds like owls are adapted to see in low light conditions. A large cornea, which is the transparent outer layer of the eye, allows a greater amount of light to enter. Similarly, a large pupil, the opening in the center of the iris, can expand significantly to let in even more light. This increased light gathering capacity ensures that more light reaches the retina, where photoreceptor cells convert it into neural signals. Consequently, the bird can form a brighter and clearer image of its surroundings, enabling it to hunt and navigate effectively in the dim light of night.
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