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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 the two mirrors. What is the radius of curvature of the convex mirror?

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Solution

The correct option is **A** 25 cm

If you cover half of the convex mirror, there is no change in the position or size of the image. Only the intensity/brightness of the image is reduced.

The image formed by the plane mirror is 10 cm to the right of the convex mirror. Therefore according to the question, the image formed by the convex mirror is also at 10 cm to the right of it.

So, u=−50 cm,v=+10 cm and we have to find f.

Using mirror formula,

f=uvu+v=12.5 cm

R=2f=25 cm

If you cover half of the convex mirror, there is no change in the position or size of the image. Only the intensity/brightness of the image is reduced.

The image formed by the plane mirror is 10 cm to the right of the convex mirror. Therefore according to the question, the image formed by the convex mirror is also at 10 cm to the right of it.

So, u=−50 cm,v=+10 cm and we have to find f.

Using mirror formula,

f=uvu+v=12.5 cm

R=2f=25 cm

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