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.
Given below are two statements:
Statement-I: If a parallel paraxial beam of light were incident on a concave mirror, making some angle with the principal axis, the reflected rays would converge at a point in focal plane.
Statement-II: Power(P) of concave mirror is positive even though focal length(f) is negative.
In the light of the above statements, choose the most appropriate answer from the options given below.
1. Both statement I and statement II are correct
2. Both statement I and statement II are incorrect
3. Statement I is correct but statement II is incorrect
4. Statement I is incorrect but statement II is correct
View Answer
Statement I is a standard result of paraxial ray optics. For Statement II, power of a mirror is given by \(P = -1/f\). Since \(f\) is negative for a concave mirror, \(P\) is positive. Thus, both statements are correct.
A convex mirror of focal length \(10\text{ cm}\) forms an image which is \(\frac{1}{3}\) times of the height of a real object. The distance of the object from the mirror is
1. \(10\text{ cm}\)
2. \(30\text{ cm}\)
3. \(20\text{ cm}\)
4. \(15\text{ cm}\)
View Answer
For a convex mirror, \(f = +10\text{ cm}\) and magnification is virtual and erect, so \(m = +\frac{1}{3}\). Using \(m = \frac{f}{f-u}\), we get \(\frac{1}{3} = \frac{10}{10-u} \implies 10-u = 30 \implies u = -20\text{ cm}\). The distance is \(20\text{ cm}\).