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(C) For a concave mirror,the focal length $f = -24 \ cm$. The mirror formula is $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$,which gives $v = \frac{uf}{u

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$(C, D)$

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(C) For a concave mirror,the focal length $f = -24 \ cm$. The mirror formula is $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$,which gives $v = \frac{uf}{u-f}$.We check the recorded values against the theoretical values calculated using the mirror formula:$1$. For $u = -42 \ cm$: $v = \frac{(-42)(-24)}{-42+24} = \frac{1008}{-18} = -56 \ cm$. (Matches)$2$. For $u = -48 \ cm$: $v = \frac{(-48)(-24)}{-48+24} = \frac{1152}{-24} = -48 \ cm$. (Matches)$3$. For $u = -60 \ cm$: $v = \frac{(-60)(-24)}{-60+24} = \frac{1440}{-36} = -40 \ cm$. (Matches)$4$. For $u = -66 \ cm$: $v = \frac{(-66)(-24)}{-66+24} = \frac{1584}{-42} \approx -37.71 \ cm$. The recorded value is $33 \ cm$. The difference $|37.71 - 33| = 4.71 \ cm$,which is much greater than the error limit of $0.2 \ cm$.$5$. For $u = -78 \ cm$: $v = \frac{(-78)(-24)}{-78+24} = \frac{1872}{-54} \approx -34.66 \ cm$. The recorded value is $39 \ cm$. The difference $|34.66 - 39| = 4.34 \ cm$,which is much greater than the error limit of $0.2 \ cm$.Thus,the data sets $(66, 33)$ and $(78, 39)$ are incorrectly recorded.

Column-$I$	Column-$II$
$1$. $m = -2$	a. Convex mirror
$2$. $m = -1/2$	b. Concave mirror
$3$. $m = +2$	c. Real image
$4$. $m = +1/2$	d. Virtual image

Similar Questions

The distance between an object and its image (magnified by $-\frac{1}{3}$) is $30 \ cm$. The focal length of the mirror used is $\left(\frac{x}{4}\right) \ cm$,where the magnitude of the value of $x$ is . . . . . . .

What will be the height of the image when an object of height $2 \ mm$ is placed on the principal axis of a convex mirror (of radius of curvature $40 \ cm$) at a distance of $20 \ cm$ from the mirror?

The focal length of a convex mirror is $20\, cm$. Its radius of curvature will be.....$cm$.

What is linear magnification? Obtain the equation of linear magnification for a concave mirror.

Match the corresponding entries of Column-$I$ with Column-$II$. [Where $m$ is the magnification produced by the mirror]
Column-$I$ Column-$II$
$1$. $m = -2$ a. Convex mirror
$2$. $m = -1/2$ b. Concave mirror
$3$. $m = +2$ c. Real image
$4$. $m = +1/2$ d. Virtual image

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