Assertion (A): There is refracting glass slab between Ram and Anoop, then Ram appears nearer to Anoop as Compared to the actual distance between them.
Reason (R): Ray of light starting from Ram will undergo two times refraction before reaching to Anoop.
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
When light rays pass from a denser medium (glass slab) to a rarer medium (air), they bend away from the normal, making the object appear closer than its actual position. This phenomenon is known as apparent depth.
Light from Ram travels through the slab, undergoing refraction at both surfaces (air to glass and glass to air), leading to this apparent shift. Both A and R are true, and R explains A.
Assertion (A): Sky appears blue.
Reason (R): Sensitivity of eye is higher for blue colour as compare to violet colour.
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
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Assertion (A) is true, sky appears blue due to Rayleigh scattering of sunlight. Reason (R) is true, the human eye has higher sensitivity to blue light than violet. However, R is a factor in perception, not the direct explanation for why blue light scatters more. Both are true, but R does not explain A.
Assertion (A): Optical fibre communication is fastest way of communication.
Reason (R): Optical interference between fibres is zero.
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
Optical fiber communication offers very high bandwidth and speed due to light's high frequency and minimal signal loss via total internal reflection. The design ensures minimal to effectively zero optical interference between fibers, which is crucial for maintaining signal integrity and enabling high data rates. Thus, both A and R are true, and R explains A.
Assertion (A): Optical path length is always greater than or equal to geometrical path length.
Reason (R): Light travels with speed of \(3 \times 10^8 \text{ m/s}\) in vacuum.
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
Optical path length \(OPL = \mu \times L\), where \(\mu\) is the refractive index and \(L\) is the geometrical path length. Since \(\mu \ge 1\) for all transparent media, \(OPL \ge L\). So (A) is true. Light travels at \(3 \times 10^8 \text{ m/s}\) in vacuum. So (R) is true. However, (R) does not explain (A); (A) is explained by the definition of refractive index (\(\mu = c/v\)) which implies \(\mu \ge 1\) because \(v \le c\). Thus, (R) is true but not the correct explanation for (A).
Assertion (A): Minimum distance between a real object and its real image formed by a convex lens is three times the focal length of lens.
Reason (R): Distance between an object and its real image formed by convex lens is minimum when magnification produced by the lens has minimum value.
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
For a convex lens, the minimum distance between a real object and its real image is \(4f\), occurring when the object is placed at \(2f\). At this point, the magnification is \(|m|=1\). The minimum magnitude of magnification approaches zero as the object moves to infinity. Hence, both Assertion (A) and Reason (R) are false.
Assertion (A): Light of wavelength \(5500 \text A^0\) travelling in medium 1 is incident on an interface and gets refracted into medium 2. Due to refraction, if it deviates by an angle \(15^{\circ}\), then its wavelength in medium 2 could be greater than or smaller than \(5500 \text{ A^0}\) but never the same.
Reason (R): As light is refracted, its colour changes.
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
During refraction, the frequency of light remains constant, which means its color does not change. However, its wavelength \(\lambda\) and speed \(v\) change such that \(n_1\lambda_1 = n_2\lambda_2\). Since the light deviates, \(n_1 \neq n_2\), implying \(\lambda_1 \neq \lambda_2\). Thus, Assertion (A) is true and Reason (R) is false.
Assertion (A): If an air bubble is trapped in a glass slab will not produce any lens action.
Reason (R): Behaviour of a shape like a lens is in dependent of surrounding medium.
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
An air bubble in a glass slab (\(n_{\text{air}} < n_{\text{glass}}\)) acts as a diverging lens, thus producing lens action. So, Assertion (A) is false. Assuming 'in dependent' is a typo for 'independent', Reason (R) 'Behaviour of a shape like a lens is independent of surrounding medium' would also be false, as lens focal length (and hence behavior) is highly dependent on the surrounding medium. Therefore, both A and R are false under this interpretation.
Assertion (A): When a light wave travels from a rarer to a denser medium, it loses energy.
Reason (R): When a light wave travels from a rarer to a denser medium, it loses speed and energy carried by the wave is proportional to its speed.
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 energy of a light wave depends on its frequency \(E=h\nu\), which remains constant when light travels between different media. While the speed changes, the energy does not. Therefore, both assertion and reason are false.
Assertion (A): When a monochromatic beam of light is incident from one medium to another, the frequency of incident, reflected and refracted rays are equal.
Reason (R): The incident, reflected and refracted rays are co-planar.
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 frequency of light is an intrinsic property of the source and remains constant upon changing media, so A is true. According to laws of reflection and refraction, the incident, reflected, and refracted rays lie in the same plane as the normal, so R is true. However, R does not explain A.
Assertion (A): The refractive index of diamond is \(\sqrt{6}\), and that of liquid is \(\sqrt{3}\), . If the light travels from diamond to the liquid, it will totally reflected when the angle of incidence is \(30^\circ\).
Reason (R): For total internal reflection, angle of incidence should be less than critical angle \(\theta_c = sin^{-1}(\frac{1}{\mu})\).
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 critical angle \(\theta_c = sin^{-1}(\mu_{liquid}/\mu_{diamond}) = sin^{-1}(\sqrt{3}/\sqrt{6}) = sin^{-1}(1/\sqrt{2}) = 45^\circ\), . For TIR, the angle of incidence (i), must be greater than \(\theta_c), (i.e., (i > 45^\circ),\). Since \(i = 30^\circ\), is not greater than \(45^\circ\), A is false. Reason R is also false because TIR occurs when \(i > \theta_c\).