Assertion (A): Focal length of a convex mirror may be negative.
Reason (R): Distances measured in the direction of incident rays may be taken as negative.
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
According to Cartesian sign convention, the focal length of a convex mirror is always positive as its principal focus is virtual and lies behind the mirror. Thus, (A) is false. While sign conventions involve directions, stating that distances measured in the direction of incident rays 'may be taken as negative' is generally incorrect or misleading; typically, these are taken as positive. Hence, (R) is also false. Thus, both (A) and (R) are false.
Assertion (A): A rectangular glass slab produces no deviation and no dispersion.
Reason (R): Dispersive power of glass slab 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
A rectangular glass slab causes no net angular deviation but does produce lateral shift. It causes dispersion for polychromatic light. So (A) is false. Glass, being a dispersive medium, has a non-zero dispersive power. So (R) is false. Thus, both (A) and (R) are false.
Assertion (A): Diamond in air shine brightly and when dipped in transparent oil, its shine reduces.
Reason (R): Diamond shines due to multiple total internal reflections.
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
Diamond's high refractive index leads to a small critical angle, causing multiple total internal reflections (TIR) and bright shine. When in oil, the refractive index difference with the surroundings decreases, increasing the critical angle, reducing TIR, and thus reducing its shine. Both (A) and (R) are true, and (R) 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): Biconvex lens can form virtual image of a virtual object.
Reason (R): Nature of lens depends on refractive index of surrounding.
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
A biconvex lens can form a virtual image of a virtual object, for instance, when intercepting converging rays. So (A) is true. The nature of a lens (converging or diverging) is determined by the refractive index of its material relative to the surrounding medium. If \(\mu_{lens} > \mu_{medium}\), a biconvex lens converges; otherwise, it diverges. So (R) is true and 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): When an object is placed between two plane parallel mirrors, all the images formed are of equal intensity.
Reason (R): In above situation of two plane parallel mirrors, only two images are possible.
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 false. Image intensity decreases with each reflection due to absorption.
Reason (R) is false. An infinite number of images are formed between two parallel plane mirrors.
Therefore, both (A) and (R) are 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.
Assertion (A): A real object is placed on the optic axis of a lens such that an erect image of twice the size of the object is obtained. The lens must then be a convergent lens.
Reason (R): Erect image of a real object can be produced by a concave lens and also by a convex lens.
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 real object producing an erect, magnified image (like (2) times) can only happen with a convergent (convex) lens when the object is between (F) and (O).
Reason (R) is true. Concave lenses produce erect, diminished images; convex lenses produce erect, magnified images under specific conditions.
Both (A) and (R) are true, but (R) does not explain the magnification condition in (A).
Assertion (A): A real object is placed on the optic axis of a lens such that magnification of the image is (+0.5). The lens must then be a divergent lens.
Reason (R): A concave lens always produces a virtual image of a real object.
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. (m = +0.5) indicates an erect and diminished image. For a real object, only a divergent (concave) lens produces such an image.
Reason (R) is true. A concave lens always forms a virtual, erect, and diminished image for a real object.
(R) correctly explains (A) because a concave lens's image characteristics match the given magnification.