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Question

An object is placed in front of a convex mirror at a distance of 50 cm. A plane mirror is introduced covering the lower half of the convex mirror. If the distance between the object and the plane mirror is 30 cm, it is found that there is no parallax between the images formed by two mirrors. The radius of curvature of the mirror will be-

A
12.5 cm
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B
25 cm
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C
503 cm
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D
18 cm
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Solution

The correct option is B 25 cm
Since, there is no parallax between the images formed by two mirrors, it means that both images by plane mirror and convex mirror are coinciding each other.



Given, Distance between the plane mirror and object=30 cmDistance between the convex mirror and object=50 cm

According to a property of plane mirror, it will form an image at a distance of 30 cm behind it.

Hence, for the convex mirror,

u=50 cm ; v=+10 cm

Using the mirror formula,

1f=1v+1u

1f=1+10+150=450

f=252 cm

R=2f=25 cm

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (B) is the correct answer.

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