A convex mirror produces an image at a distance of 20 cm from the mirror for an object placed at 40 cm . find the circumference of the sphere of which convex mirror is a part.

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>>An object is placed at a distance of 20

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An object is placed at a distance of 20 cm from a convex mirror or radius of curvature 40 cm. At what distance from the object should a plane mirror be placed so that the images due to the mirror and the plane mirror are in the same plane?

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Correct option is A)

Given: An object is placed at a distance of 20 cm from a convex mirror or radius of curvature 40 cm.

To find the distance at which the plane mirror should be placed such that the images due to the mirror and the plane mirror are in the same plane

Solution:

According to the given criteria,

Object distance from convex mirror, u=−20cm

Radius of curvature of convex mirror, R=40cm

Focal length of the convex mirror, f=

2

R

=

2

40

=20cm

Now applying the mirror formula we get,

f

1

=

v

1

+

u

1

⟹

20

1

=

v

1

+

−20

1

⟹

v

1

=

20

1

+

20

1

⟹v=10cm

So the distance is formed on the opposite side of the object at a distance of 10 cm from the mirror as shown in above fig.

The distance between object and image is u+v=20+10=30cm

When plane mirror is placed in front of object and in order to get image at same position as convex mirror, the mirror should be place at

2

30

=15cm, as in plane mirror the object distance from mirror is equal to image distance from the plane mirror (refer above fig).

Hence the distance at which the plane mirror should be placed such that the images due to the mirror and the plane mirror are in the same plane = 15cm