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
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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.
Assertion (A): Warning signals installed at the top of tall buildings and monuments employ red light.
Reason (R): Human eye is most sensitive to red 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
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Red light has the longest wavelength and scatters least, making it visible from a distance. Thus, (A) is true. However, the human eye is most sensitive to yellow-green light (approximately \(555\text{ nm}\)), not red. Thus, (R) is false. So, (A) is true but (R) is false.
Assertion (A): A convex lens suffers from chromatic aberration.
Reason (R): All parallel rays of monochromatic light passing through a convex lens do not come to a focus at the same point.
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
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A single convex lens suffers from chromatic aberration due to dispersion, so (A) is true. For monochromatic light, ideal parallel rays passing through a convex lens *do* converge at a single focal point (ignoring spherical aberration). Hence, (R) is false.
Assertion (A): The Focal length of lens is same for all colours of light
Reason (R): The focal length depends only upon the material of the 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
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The focal length of a lens is given by \(1/f = (n-1)(1/R_1 - 1/R_2)\). Since the refractive index \(n\) varies with the color of light, focal length is different for different colors. Thus (A) is false. Focal length depends on \(n\), \(R_1\), \(R_2\), and the surrounding medium, not only the material. Also, \(n\) for a material depends on color. So (R) is false. Both (A) and (R) are false.
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.
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): 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.