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): 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): A completely transparent material will be invisible in vacuum, when the refractive index is unity.
Reason (R): The ratio of the refractive index of red light to blue light in vacuum is less than unity.
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 material's refractive index matches the surrounding (vacuum, \(\mu=1\)), light passes through without deviation or reflection, making it invisible. Reason (R) is false; in vacuum, the refractive index is \(1\) for all colors, so their ratio is \(1\), not less than unity. Thus, A is true and R is false.
Assertion (A): For every observer rainbow is a personal one.
Reason (R): Every observer intercepts light from same water drops.
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; a rainbow's apparent position depends on the observer's location and the specific light rays from water droplets they intercept. Reason (R) is false; different observers see rainbows formed by light from *different* sets of water drops at different angles. Thus, A is true and R is false.
Assertion (A): The persistence of vision \(1/16\) second is used in cinematography.
Reason (R): The human eye forms the real image of an object at its retina.
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 brain's retention of images for about \(1/16\) second creates motion from rapid stills. Reason (R) is true; the eye's lens system forms a real, inverted image on the retina. R describes a fundamental eye function, which is a prerequisite for A but not its direct explanation. Thus, both are true, but 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.
Assertion (A): Blue colour of sky is due to scattering.
Reason (R): According to Rayleigh blue colour shows more scattering 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, blue sky is a result of Rayleigh scattering. Reason (R) is false; Rayleigh scattering is inversely proportional to the fourth power of wavelength (\(1/lambda^4\)), meaning violet light (shorter wavelength) scatters more than blue light. Thus, A is true and R is false.
Assertion (A): A convex lens of glass \(\mu = 1.5\) behave as a diverging lens when immersed in carbon disulphide of higher refractive index \(\mu = 1.65\).
Reason (R): A diverging lens is thinner in the middle and thicker at the edges.
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; a lens acts as a diverging lens if the surrounding medium's refractive index is greater than the lens material's. Reason (R) is true; a concave lens (a common diverging lens) has this shape. R describes the shape of a diverging lens, not why a convex lens changes its behavior in a different medium. Thus, both are true, but R does not explain A.