Assertion (A): If an object is placed between (f) and (2f) of a convex lens, a real image can be seen on a screen placed at image location. If the screen is removed then image will not be seen.
Reason (R): Real image of a object can not formed in air.
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 real image is formed by the actual intersection of light rays and exists in space independently of a screen. It can be viewed by the eye even without a screen. Real images are formed in the medium where rays converge, typically air. Therefore, both assertion and reason are false.
Assertion (A): Optical fibre communication is fastest way of communication.
Reason (R): Optical interference between fibres 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
Optical fiber communication offers very high bandwidth and speed due to light's high frequency and minimal signal loss via total internal reflection. The design ensures minimal to effectively zero optical interference between fibers, which is crucial for maintaining signal integrity and enabling high data rates. Thus, both A and R are true, and R explains A.
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): 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 point object is placed at a distance of \(26 \text{ cm}\) from a convex mirror of focal length \(26 \text{ cm}\). The image will form at infinity.
Reason (R): For above given system the equation \(\frac{1}{v} – \frac{1}{u} = \frac{1}{f}\) gives position of 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
For a convex mirror, focal length \(f = +26 \text{ cm}\). Object distance \(u = -26 \text{ cm}\). Using mirror formula \(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\) gives \(\frac{1}{v} = \frac{1}{26} - \frac{1}{-26} = \frac{2}{26} = \frac{1}{13}\) so \(v = 13 \text{ cm}\). (A) is false. The correct mirror formula is \(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\) not \(\frac{1}{v} - \frac{1}{u} = \frac{1}{f}\). (R) is false. Thus, both (A) and (R) are false.