Assertion (A): A ray of white light shows no dispersion on emerging from a glass slab although there occurs dispersion inside the glass slab.
Reason (R): The velocity of light inside the glass slab is same for all different colours.
Assertion (A) is true; due to the parallel surfaces of the glass slab, the dispersed colors recombine upon emerging, showing no net dispersion. Reason (R) is false; dispersion occurs precisely because the velocity of light (and thus refractive index) varies for different colors within the medium. Thus, A is true and R is false.
Assertion (A): Warning signals installed at the top of tall buildings and monuments employ red light.
Reason (R): Human eye is most sensitive to red colour.
Red light has the longest wavelength and scatters least, making it visible from a distance. Thus, (A) is true. However, the human eye is most sensitive to yellow-green light (approximately \(555\text{ nm}\)), not red. Thus, (R) is false. So, (A) is true but (R) is false.
Assertion (A): A single lens cannot be free from chromatic aberration.
Reason (R): When light passes through single lens dispersion must occur.
Chromatic aberration occurs because the refractive index of a lens material varies with wavelength (dispersion). A single lens always causes dispersion, leading to different focal points for different colors. Thus, both (A) and (R) are true, and (R) explains (A).
Assertion (A): When white light passes through a prism, deviation of violet light is more than green light.
Reason (R): In a prism average deviation is measured as deviation of yellow light.
Violet light has the highest refractive index in a prism, so it deviates most, hence (A) is true. Yellow light is generally used for average deviation calculations in dispersion, so (R) is true. However, (R) does not explain (A).
Assertion (A): Law of reflection is applicable for all type of mirrors.
Reason (R): Rays which are parallel to principal axis are known as paraxial rays.
Laws of reflection are fundamental and apply to all mirrors, so (A) is true. Paraxial rays are rays close and parallel to the principal axis, so (R) is true. (R) defines a term, it does not explain the universality of reflection laws.
Assertion (A): A convex lens suffers from chromatic aberration.
Reason (R): All parallel rays of monochromatic light passing through a convex lens do not come to a focus at the same point.
A single convex lens suffers from chromatic aberration due to dispersion, so (A) is true. For monochromatic light, ideal parallel rays passing through a convex lens *do* converge at a single focal point (ignoring spherical aberration). Hence, (R) is false.
Assertion (A): If an object moves in front of a concave mirror parallel to principal axis. The angle between the object velocity and image velocity can never be acute.
Reason (R): Object velocity and image velocity perpendicular to principal axis for spherical mirror is not same.
If an object moves along the principal axis, its image also moves along it, with velocities always anti-parallel (angle \(180^\circ\)), so (A) is true. Perpendicular components of velocity are related by \(v_{iy} = m v_{oy}\), where magnification \(m\) is generally not 1, so (R) is true. (R) does not explain (A).
Assertion (A): The Focal length of lens is same for all colours of light
Reason (R): The focal length depends only upon the material of the lens
The focal length of a lens is given by \(1/f = (n-1)(1/R_1 - 1/R_2)\). Since the refractive index \(n\) varies with the color of light, focal length is different for different colors. Thus (A) is false. Focal length depends on \(n\), \(R_1\), \(R_2\), and the surrounding medium, not only the material. Also, \(n\) for a material depends on color. So (R) is false. Both (A) and (R) are false.
Assertion (A): When light moves from a denser medium to rarer medium then Snell’s law can’t satisfied for all angle of incidence.
Reason (R): When light moves from denser to rarer medium, for angle of incidence greater than the critical angle, no refraction is possible.
Total internal reflection occurs when light travels from a denser to a rarer medium, and the angle of incidence (theta_i) is greater than the critical angle (theta_c). In this case, (sintheta_r) from Snell's law becomes greater than 1, implying no refraction is possible. Thus, Snell's law is not satisfied for all incidence angles, and the reason correctly explains this phenomenon.
Assertion (A): On hot summer days, optical density of different layer of air increases with height from ground.
Reason (R): Refractive index of air increases with its density.
On hot summer days, air near the ground is hotter and less dense. As height increases, air becomes cooler and denser. Since refractive index (and thus optical density) increases with density, the optical density of air layers increases with height. Therefore, both assertion and reason are true, and the reason explains the assertion.