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 \(i > \theta_c\).
Assertion (A): The speed of light in an optically rarer medium is greater than that in an optically denser medium.
Reason (R): One light year equals to \(9.5 \times 10^{12}\), km.
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 optically rarer medium has a lower refractive index, meaning light travels faster in it, so A is true. A light-year is the distance light travels in one year, approximately \(9.46 \times 10^{12}\), km, so R is true. However, the definition of a light-year does not explain the speed of light in different media.
Assertion (A): Consider a prism A of refracting angle \(5^0\), and another prism B of refracting angle \(10^0\), . Both prisms are made of crown glass. If white light is incident on each prism, angular dispersion caused by prism B will be more.
Reason (R): Dispersive power depends on the nature material.
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
Angular dispersion is given by \(\delta = (\mu_v - \mu_r)A\), . Since both prisms are of the same material, \((\mu_v - \mu_r\),), is constant. Prism B has a larger angle (A), \((10^\circ\), vs \(5^\circ\),), so it will cause more angular dispersion, making A true. Dispersive power is indeed a property of the material, so R is true. However, R does not explain why prism B has more dispersion than A, which is due to its larger refracting angle.