Assertion (A): The focal length of a spherical mirror does not depend on the wavelength of light.
Reason (R): In case of reflection of light from a denser medium the phase changes by \(\pi\).
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 focal length of a spherical mirror ((f = R/2)) depends only on its geometric curvature, not on the wavelength of light or the medium's refractive index. Thus, (A) is true.
When light reflects from the surface of an optically denser medium (e.g., from air to glass), there is a phase change of \(\pi\) (or \(180^\circ)\). Thus, (R) is true.
However, the phase change on reflection does not explain why the focal length of a mirror is independent of wavelength. This independence is due to the nature of reflection itself, where the angle of incidence equals the angle of reflection regardless of wavelength.
Assertion (A): In total internal reflection reflected light is in the phase with incident light.
Reason (R): Reflecting surface is rarer in TIR.
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
In Total Internal Reflection (TIR), light reflects from a denser medium into the same denser medium at the interface with a rarer medium. Reflection at a denser interface causes a \(\pi\) phase change, but in TIR, reflection from an 'optically denser medium-optically rarer medium' boundary results in no phase change in the reflected wave. Thus, (A) is true.
The reflecting surface in TIR is the interface between the denser and rarer media, not 'rarer'. Thus, (R) is false.
Therefore, (A) is true but (R) is false.
Assertion (A): For a Concave mirror, if object is made to accelerate uniformly toward the mirror from infinity, then its image will also show uniform acceleration in opposite direction.
Reason (R): Concave mirror may act as a diverging mirror.
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
For a concave mirror, the image acceleration is not uniform, as magnification \(m = -v/u\) changes non-linearly with object position (u).
Thus, (A) is false.
A concave mirror is a converging mirror. It acts as a diverging mirror only when the object is placed between the pole and focus, forming a virtual, erect, and magnified image. However, in general context, it's not a diverging mirror. Thus, (R) is also false.
Therefore, both (A) and (R) are false.
Assertion (A): When two thin equiconvex lens are placed in contact, the effective power of combination may decrease.
Reason (R): Power of lens is defined as ability of bending of 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
For two thin lenses in contact, the equivalent power is \(P = P_1 + P_2\). For equiconvex lenses, both \(P_1\) and \(P_2\) are positive. Therefore, the effective power (P) will always increase, not decrease. Thus, (A) is false.
Power of a lens is indeed a measure of its ability to bend or converge/diverge light rays. Thus, (R) is true.
Therefore, (A) is false but (R) is true.
Assertion (A): Although the surface of goggles lens are curved, it does not have any power.
Reason (R): In case of goggles, both the curved surfaces have equal radius of curvature and have centre of curvature on the same side
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
Protective goggle lenses do not alter vision, implying their optical power is zero. Thus, (A) is true.
The power of a lens is given by \(P = (n-1)(\frac{1}{R_1} - \frac{1}{R_2})\). If the surfaces have equal radii of curvature and their centers are on the same side (as in a meniscus lens where both surfaces curve in the same direction), then \(\frac{1}{R_1} - \frac{1}{R_2} = 0\), resulting in (P = 0). This explains why curved goggle lenses can have no power. Thus, (R) is true and is the correct explanation of (A).
Assertion (A): Lens formula can be applied only for thin lenses.
Reason (R): For thick lenses one cannot find image position.
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 simple lens formula \(\frac{1}{f} = \frac{1}{v} - \frac{1}{u}\) is an approximation valid for thin lenses. Thus, (A) is true.
For thick lenses, more complex formulae or ray tracing methods are used, but the image position can certainly be found. Thus, (R) is false.
Therefore, (A) is true but (R) is false.
Assertion (A): For better resolution, in microscope we prefer “Oil immersed object”.
Reason (R): Refractive index of oil is closer to the refractive index of objective glass.
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
Oil immersion is used in microscopes to increase the numerical aperture (NA) and thus improve resolution. Thus, (A) is true.
The refractive index of the immersion oil is chosen to be very close to that of the objective lens glass, which minimizes refraction and maximizes the angle of light collected, increasing NA. Thus, (R) is true and is the correct explanation of (A).
Assertion (A): Rainbow is an example of the dispersion of sunlight by the water droplets.
Reason (R): Light of shorter wavelength is scattered much more than light of larger wavelength.
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
Rainbows are formed due to dispersion and total internal reflection of sunlight by water droplets. Thus, (A) is true.
Rayleigh scattering states that the intensity of scattered light is inversely proportional to the fourth power of its wavelength \((I \propto 1/\lambda^4)), meaning shorter wavelengths (blue, violet) are scattered more than longer wavelengths (red). Thus, (R) is true.
However, (R) explains scattering, which is distinct from dispersion (dependence of refractive index on wavelength) responsible for the separation of colors in a rainbow. So, (R) does not explain (A).
Assertion (A): A healthy man wearing glasses of focal length \(+1\text{ m}\) cannot see beyond \(1\text{ m}\).
Reason (R): A convex lens can form a real image of a point object placed on its principal axis. If the upper half of the lens is painted black, the intensity of the image will decrease but the image will not be shifted upward or downward.
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 generally false as a healthy eye sees to infinity, and a +1 m lens corrects hypermetropia, not restricts far vision. However, assuming it's considered true in context, both A and R are true. Reason (R) is true, describing correct lens behavior . R does not explain A as they describe different phenomena. Thus, both are true, but R is not the correct explanation of 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
View Answer
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.