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Q.

Converging rays are incident on a convex spherical mirror so that their extensions intersect 30cm behind the mirror on the optical axis. The reflected rays form a diverging beam, so that their extensions intersect the optical axis 1.2m from the mirror. The focal length of the mirror is


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a

40cm 

b

60cm 

c

30cm 

d

24cm 

answer is D.

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Detailed Solution

Concept: The mirror is said to be convex if the surface of the sphere has been silvered so that it can reflect light. The line that runs from the surface of the mirror to the centre of the original sphere is known as the optic axis, and the centre of that sphere is known as the centre of curvature (C). The focus of the mirror is the location on the primary axis where all incident and refracted rays converge. Keep in mind that the focus and the centre of curvature are situated on the mirror's side that is behind the convex mirror.
When the reflected rays diverge so that their extensions intersect at a point, then that point is our image and the distance of that image from the centre of curvature is called image distance. Object distance is denoted as u and image distance is denoted as Question Image. The focal length (f) of the mirror can be obtained from the mirror formula as follows:
Question ImageQuestion ImageQuestion ImageHence, the correct option is 4.
 
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Converging rays are incident on a convex spherical mirror so that their extensions intersect 30cm behind the mirror on the optical axis. The reflected rays form a diverging beam, so that their extensions intersect the optical axis 1.2m from the mirror. The focal length of the mirror is