Ray Optics And Optical Instruments

Explanation
The refractive index of water with respect to glass can be calculated by dividing the refractive index of glass by the refractive index of water. In this case, the refractive index of glass is 1.5 and the refractive index of water is 1.3. Therefore, the refractive index of water with respect to glass is 1.5/1.3, which is not equal to any of the given options.

Explanation
The power of a lens is determined by its focal length. The formula to calculate the power of a lens is P = 1/f, where P is the power and f is the focal length. In this case, the focal length of the lens is given as 50 cm. Plugging this value into the formula, we get P = 1/50 = 0.02 D. However, the answer options do not include this value. The closest option is + 2 D, which is the correct answer.

Explanation
When a real object is placed at a distance equal to the focal length of a convex mirror, the image formed is virtual, erect, and diminished in size. Therefore, the correct answer is "Infinity" because the image is formed at an infinite distance from the mirror.

Explanation
When a convex lens and a concave lens are placed in contact, they act as one lens. The focal length of the combination can be found by using the lens formula: 1/f = 1/f1 + 1/f2, where f1 and f2 are the focal lengths of the individual lenses. Since the convex lens has a positive focal length (x) and the concave lens has a negative focal length (y), when they are added together, the negative focal length cancels out the positive focal length. Therefore, the focal length of the combination is x - y.

Explanation
The correct variation is shown by a straight line passing through the origin. This is because according to the law of reflection, the angle of incidence is equal to the angle of reflection. Therefore, as the angle of incidence increases, the angle of reflection also increases in a linear manner. This linear relationship is represented by a straight line on the graph.

Explanation
The correct answer is "Option C: Convex". When a water drop is placed between two glass plates, it forms a convex shape due to surface tension. Surface tension is the force that acts on the surface of a liquid and causes it to behave like a stretched elastic sheet. In the case of a water drop, the surface tension pulls the water molecules inward, causing the drop to take on a rounded shape. This convex shape is correctly shown in option C.

Explanation
When a light beam is incident normally on the face AB of the glass prism, it enters the prism without any deviation. As the refractive index of the prism is greater than that of water, the light beam will bend away from the normal when it reaches the face BC. In order for the light beam to be totally reflected at the face BC, the angle of incidence (C) must be such that sin C is equal to the ratio of the refractive indices of water and the prism (4/3 / 1.5 = 8/9). Therefore, the correct answer is sin C = 8/9.

Explanation
The graph for the experiment to find the focal length of a concave mirror shows a linear relationship between the magnitude of the object distance (u) and the image distance (v). This indicates that the mirror obeys the mirror formula, which states that 1/f = 1/u + 1/v, where f is the focal length of the mirror. The graph shows that as the object distance increases, the image distance also increases, suggesting that the focal length of the concave mirror is positive. Therefore, the correct answer is a straight line passing through the origin.

Explanation
The refractive index of a completely transparent medium should be 1 for it to be visible in vacuum. This is because the refractive index determines how much light is bent or refracted when it passes through a medium. In vacuum, where there is no medium to refract the light, the refractive index should be 1 so that the light can travel in a straight line and be visible to the observer.

Explanation
A rainbow is formed when sunlight is refracted, or bent, as it enters a raindrop, and then dispersed, or separated into its different colors, as it exits the raindrop. This dispersion occurs because the different colors of light have different wavelengths and therefore bend at different angles. Total internal reflection then takes place when the dispersed light reflects off the inside surface of the raindrop and exits at a different angle. This combination of dispersion and total internal reflection is what creates the beautiful array of colors that we see in a rainbow.

Explanation
The correct answer is Concave, f = 10 cm. When the plane face of a plano-convex lens is silvered, it acts as a concave mirror. The focal length of the mirror is equal to the radius of curvature of the curved surface of the lens, which is 10 cm in this case. Therefore, the mirror behaves as a concave mirror with a focal length of 10 cm.

Explanation
The ability of a telescope to resolve two objects depends on the wavelength of light and the diameter of the objective lens. The minimum distance that can be resolved is given by the formula: minimum distance = 1.22 * wavelength / diameter. In this case, the mean wavelength of light is 5000 Ǻ and the diameter of the objective lens is 10 cm. Plugging these values into the formula, we get a minimum distance of approximately 5 mm. Therefore, the correct answer is 5 mm.

Explanation
When a glass lens is immersed in water, its focal length changes due to the change in refractive index. The refractive index of water is greater than that of air. As a result, the lens behaves as if it has a shorter focal length when immersed in water. Since the initial focal length in air is 2 cm, the focal length when immersed in water would be greater than 2 cm. Among the given options, the only value that satisfies this condition is 8 cm. Therefore, the correct answer is 8 cm.

Explanation
When a beam of light passes from air to glass, it undergoes a change in speed due to the change in the medium. The speed of light is slower in glass compared to air because the glass has a higher refractive index. This change in speed causes the light to decrease its velocity, resulting in a decrease in the speed of light.