Question

An object AB is placed parallel and close to the optical axis between focus F and center of curvature C of a converging mirror of focal length f as shown in the figure.

Then which of the following statements are correct?
A. Image of A will be closer to than that of B from the mirror
B. Image of AB will be parallel to the optical axis
C. Image of AB will be a straight line inclined to the optical axis
D. Image of AB will be not be a straight line

Answer 1

Hint: In the above question, the object AB is placed in front of a converging mirror and in case of a converging mirror, the image of a point closer to the focus is formed farther. The point B is nearer than A to the lens therefore the transverse magnification of B greater than A.

Complete step-by-step answer:
According to question
The object AB is placed in front of a concave mirror which is a converging mirror. In the case of a converging mirror, the image of a point of object placed nearer to the focus of the mirror is formed farther from the mirror.
Since the point B is closer to the focus, the corresponding image formed will be nearer to the infinity.
The point A is closer to the center of curvature, so the formed image will be closer to the center of curvature itself.
The above two statement can be justified with the mirror formula given by,
$\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$
Where
v = distance of image from mirror
u = distance of the object from mirror
f = distance of focus from mirror
When u tends to f then v tends to infinity that is an image of the point formed near the infinity point.
Similarly when u tends to 2f then v tends to 2f itself that the point placed at center of curvature then the image is formed at center of curvature itself.
Hence the image of A will be closer than that of B from the mirror.
Also we know that the point B is placed nearer than point A to the mirror therefore the transverse magnification of B will be greater than the transverse magnification of A by the formula given by
$m = \dfrac{v}{u}$
Where m stands for magnification of the mirror.
Hence the transverse magnification of B is greater than transverse magnification of A
Therefore the image size of point B of the object will be greater than the image size of point A.
Hence the image will be a straight line inclined to the optical axis.
Therefore the correct options are A and C.

Note: Generally there are two types of magnification, transverse and longitudinal magnification. The transverse magnification is defined as the ratio of the height of the image to the height of the object. On the other hand, the longitudinal magnification is defined as the ratio of the width of the image to that of the object. Magnification can be positive as well as negative.