Assertion (A): If three polarisers are arranged such that the axis of any two successive polarisers make equal angle with each other. If unpolarised light of intensity \(I_0\) incident on first polariser then intensity of emergent light after 3rd polariser is \(\frac{I_0}{8}\). If angle between them is \(45^\circ\).
Reason (R): Each time intensity becomes \(50%\) by Malus law.
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. Intensity after 1st polariser is \(I_1 = I_0/2\). Given angle between successive polarisers is \(\theta = 45^\circ\). By Malus' Law, \(I_2 = I_1 \cos^2(45^\circ) = (I_0/2)(1/2) = I_0/4\). \(I_3 = I_2 \cos^2(45^\circ) = (I_0/4)(1/2) = I_0/8\). Reason (R) is false. Intensity becomes 50% only when \(cos^2\theta = 0.5\) (i.e., \(\theta = 45^\circ\)) and only for polarized light. The first polarizer reduces unpolarized light to 50% without \(cos^2\theta\) dependence. So, the general statement 'each time intensity becomes 50%' is false.
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. 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
The resolving power of a telescope is determined by the objective lens's diameter. The eyepiece's function is to magnify the image formed by the objective, not to enhance its resolution. Thus, details not resolved by the objective cannot be resolved by the eyepiece. Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
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): 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): 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): Wave nature can be proved by phenomena of interference and diffraction.
Reason (R): Only transverse wave can show the phenomena of polarization.
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. Interference and diffraction are characteristic wave phenomena, providing strong evidence for the wave nature of light.
Reason (R) is true. Polarization is a property exclusive to transverse waves, where oscillations are perpendicular to the propagation direction.
Reason (R) describes a unique property of transverse waves, which is distinct from demonstrating wave nature via interference/diffraction. Thus, (R) does not explain (A).
Assertion (A): Radio waves cannot be diffracted by the buildings.
Reason (R): The wavelength of radio waves is very small.
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
Radio waves have wavelengths comparable to or larger than buildings \( \text{meters to kilometers}\), enabling them to diffract easily around obstacles. Thus, A is false. The wavelength of radio waves is large, not small. Thus, R is false.
Assertion (A): The plane of polarization of reflected ray is parallel to the refracting surface, when light is incident at polarising angle.
Reason (R): Vibration of electric field in refracted ray ceases about plane parallel to refracting surface.
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
At the polarizing angle (Brewster's angle), the reflected light is completely plane-polarized with its electric field vibrations perpendicular to the plane of incidence (i.e., parallel to the refracting surface). Thus, A is true. The refracted ray is partially polarized and still has electric field vibrations in various planes, not ceasing in any specific plane. Thus, R is false.