Assertion (A): As angle subtended by the diameter of objective lens at the focus of microscope increased, resolving limit also increases.
Reason (R): Resolving limit proportional to tangent of the angle subtended by the diameter of objective lens at the focus of microscope.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
The resolving limit of a microscope is \(\text{RL} = \frac{\lambda}{\text{2n} \sin\theta}\). As the angle \(\theta\) increases, \(sin\theta\) increases, causing \(\text{RL}\) to decrease (better resolution). So, Assertion (A) is false. Reason (R) is also false as \(\text{RL}\) is inversely proportional to \(sin\theta\), not proportional to \(tan\theta\).
Assertion (A): When refractive index of medium is increased resolving power also increases.
Reason (R): In medium of higher refractive index wavelength is higher.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
The resolving power of a microscope is \(\text{R.P.} = \frac{\text{2n} \sin\theta}{\lambda}\) (wavelength in vacuum). It is directly proportional to refractive index \(\text{n}\), so (A) is true. Wavelength in a medium is \(\lambda_\text{medium} = \frac{\lambda_\text{vacuum}}{\text{n}}\). Higher \(\text{n}\)
Assertion (A): The resolving power of a telescope is more if the diameter of the objective in more.
Reason (R): Objective lens of larger focal length collect more light.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
The resolving power of a telescope is \(\text{R.P.} = \frac{\text{D}}{\text{1.22}\lambda}\) where \(\text{D}\) is the diameter. Thus, larger \(\text{D}\) means higher \(\text{R.P.}), so (A) is true. Light collection depends on aperture (diameter), not directly on focal length. So, Reason (R) is false.
Assertion (A): In single slit diffraction arrangement, instead of keeping the screen far away, often a converging lens is placed after the slit and a screen is placed at its focus.
Reason (R): Lens doesn’t introduce any extra path difference for a parallel beam.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Assertion (A) is true. Using a converging lens to focus the diffraction pattern at its focal plane is standard for Fraunhofer diffraction, simulating far-field conditions. Reason (R) is false. A lens works by introducing varying optical path lengths across its aperture to achieve focusing, thus creating path differences.
Assertion (A): The stars which are not resolved in the image produced by the objective of a telescope can’t be further resolved by its eye piece.
Reason (R): The primary purpose of eyepiece of telescope is to provide the magnification of image produced by the objective.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Assertion (A) is true. The resolving power is determined by the objective; the eyepiece only magnifies the existing image, it cannot resolve features not already resolved by the objective. Reason (R) is true; the eyepiece's primary role is magnification. Reason (R) correctly explains Assertion (A).
Assertion (A): Huygens’s principle can explain converging nature of convex lens.
Reason (R): Snell’s law can be derived from Huygens’s principle.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true. Huygens' principle, through its explanation of wavefront changes, can explain how a convex lens converges light.
Reason (R) is true. Snell's law of refraction, which governs how light behaves at interfaces, can be derived directly from Huygens' principle.
Reason (R) explains a fundamental principle (Snell's Law) that underpins the behavior of lenses, thus it correctly explains (A).
Assertion (A): In a YDSE, the two slits are at distance ‘a’ apart. Interference pattern is observed on a screen at a distance D from the slits. At a point on the screen which is directly opposite to the slit, a dark fringe is observed. Then the wavelength of wave is proportional to square of distance between slits.
Reason (R): The light ray coming from two slits do not interfere at the screen.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true. If a dark fringe occurs at \(y = a/2\) (point opposite one slit), the path difference is \(a^2/(2D)\). For a dark fringe, \(a^2/(2D) = (n + 1/2)\lambda\), implying \(lambda \propto a^2\).
Reason (R) is false. The core principle of YDSE is the interference of light waves from two coherent slits, which produces the observed pattern on the screen.
Assertion (A): When a monochromatic light beam is incident normally on a reflective surface, under some condition it is possible that all lights is transmitted without any reflection.
Reason (R): When light after passing through a polaroid is incident on a reflecting surface at angle of incidence equals to polarizing angle, then all light gets transmitted without any reflection.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is false. Total transmission at normal incidence on a reflective surface is only possible if the refractive indices are identical, implying no actual reflection.
Reason (R) is false. At Brewster's angle, only the p-polarized component of light is completely transmitted. If the light passed by the polaroid is s-polarized, it would be reflected. Therefore, the statement 'all light gets transmitted' is not universally true for light passed by a polaroid without specifying its polarization.
Thus, both (A) and (R) are false.
Assertion (A): Two persons separated by a \(7\text{ m}\) partition wall in a room of \(10\text{ m}\) high can heard each other easily but cannot see each other.
Reason (R): Any sound wave can bend by the obstacle while light can’t.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true. This is a common observation due to the differing wavelengths of sound and light.
Reason (R) is true. Sound waves have longer wavelengths than light waves, causing them to diffract (bend) significantly around common obstacles. Light waves also diffract, but negligibly so for large obstacles like walls.
Reason (R) correctly explains Assertion (A).
Assertion (A): The fringe pattern in Young’s double slit experiment is result of both phenomena of interference and diffraction.
Reason (R): Diffraction results from superposition of wavelets of same wavefront.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true. The YDSE pattern is an interference pattern modulated by the diffraction pattern from each individual slit.
Reason (R) is true. Diffraction is explained by Huygens' principle, where secondary wavelets from the same wavefront superpose.
Reason (R) defines diffraction but does not explain why both interference and diffraction contribute to the YDSE pattern, so it's not the correct explanation.