Assertion (A): Rear view mirror of a vehicle is a convex mirror.
Reason (R): It never makes real image of real objects.
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
Convex mirrors are used as rear-view mirrors because they provide a wider field of view and always form virtual, erect, and diminished images of real objects. This property is crucial for drivers to see a larger area behind the vehicle and perceive objects as being further away. Both A and R are true, and R correctly explains the suitability of convex mirrors for this application.
Assertion (A): If one half of a mirror is covered by an opaque material, then only half image of the object is formed.
Reason (R): By covering one half of the mirror, focal length of mirror will be halved.
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
Covering half a mirror reduces the intensity of the image but a complete image is still formed. The focal length of a mirror depends only on its radius of curvature, not on the aperture or how much of its surface is exposed.
Assertion (A): Concave mirror can’t form virtual image of a virtual object.
Reason (R): Convex mirror can’t form real image of a real object.
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
Both Assertion (A) and Reason (R) are false. A concave mirror can form a virtual image of a virtual object if the object is between its pole and focus. A convex mirror can form a real image of a virtual object, for example, if the virtual object is placed between its pole and focus.
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): 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): If an object moves in front of a concave mirror parallel to principal axis. The angle between the object velocity and image velocity can never be acute.
Reason (R): Object velocity and image velocity perpendicular to principal axis for spherical mirror is not same.
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
If an object moves along the principal axis, its image also moves along it, with velocities always anti-parallel (angle \(180^\circ\)), so (A) is true. Perpendicular components of velocity are related by \(v_{iy} = m v_{oy}\), where magnification \(m\) is generally not 1, so (R) is true. (R) does not explain (A).
Assertion (A): The formula \(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\) connecting u and v for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvatures.
Reason (R): Laws of reflection are strictly valid for smaller size of optical system.
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
Mirror formula \(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\) is valid under paraxial approximation, which requires small aperture mirrors. Laws of reflection are fundamental, and their simplified application in the mirror formula relies on paraxial rays. Thus, both (A) and (R) are true, and (R) correctly explains (A).
Assertion (A): A plano-convex lens is silvered at plane surface. It can act as a converging mirror.
Reason (R): Focal length of concave mirror is independent of 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
When a plano-convex lens is silvered on its plane surface, it forms a lens-mirror combination that behaves as a converging mirror. So (A) is true. The focal length of a spherical mirror (concave or convex) depends only on its radius of curvature and not on the surrounding medium. So (R) is false. Thus (A) is true but (R) is false.
Assertion (A): A dentist uses a concave mirror to examine a small cavity.
Reason (R): A concave mirror always forms a magnified and erect image.
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; dentists use concave mirrors for magnified virtual images.
Reason (R) is false as a concave mirror forms magnified and erect images only when the object is between the pole and focal point. It can also form real and inverted images.
Thus, (A) is true and (R) is false.
Assertion (A): The focal length of spherical mirror does not depend on the wavelength of light.
Reason (R): The number of wavelengths in the visible region of spectrum are infinite.
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 as focal length of spherical mirrors depends only on its radius of curvature, not refractive index or wavelength.
Reason (R) is false. The visible spectrum is a continuous range, not an infinite countable number of wavelengths.
So, (A) is true but (R) is false.