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.
Assertion (A): A concave mirror and a concave lens have the same focal length in air. When dipped in water, the focal length of the two are equal.
Reason (R): The focal length depends only on the radii of curvature.
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
The focal length of a mirror \(f_m = R/2\) depends only on its radius of curvature and is independent of the surrounding medium. The focal length of a lens \(1/f_l = (n_l/n_m - 1)(1/R_1 - 1/R_2)\) depends on the refractive indices of the lens material (\(n_l\)) and the surrounding medium (\(n_m\)), as well as radii of curvature. Thus, Assertion (A) is false as their focal lengths are generally not equal and lens focal length changes with medium. Reason (R) is false as lens focal length also depends on refractive indices.