An object of 10 cm in height is located 29.6 cm from the surface of a convex mir

Question

An object of 10 cm in height is located 29.6 cm from the surface of a convex mirror. The convex mirror forms an image. The same object is now located 25.6 cm in front of a plane mirror. This plane mirror also forms an image. In both cases the object is located at x = 0. The mirrors lie along the positive x axis. Both images formed in the two mirrors lie at the same x coordinate. Calculate the radius of curvature of the convex mirror. (Include the sign of the value in your answer.) ___________ cm

Explanation / Answer

From the Laws of Reflection, we know that the Plane Mirror always forms an Image of an object at the same distance behind the mirror as the object is in front of the mirror.

Hence, in our Case, the Image should be Formed at a distance of 25.6cm behind the plane mirror, which itself is placed at x= 25.6cm.

Therefore, the image will be formed at x= (25.6*2cm) = 51.2cm from x=0.

Now, in the case of the convex mirror, the mirror is placed at x= 29.6cm

And as concluded above, the image will be formed at x= 51.2cm

Also, the object is placed at x=0

Hence, the Object Ditance, u = -29.6cm( opposite to the direction of Incident light from the Pole of the convex mirror)

Image Distance, v = ( 51.2-29.6)cm = +21.6cm( in the direction of Incident light from the Pole of the convex mirror)

Using the Mirror formula, we have :

1/u + 1/v = 1/f, where f = focal length of the mirror

-> 1/f = 1/(-29.6) + 1/21.6 = 0.0125

-> f = +80cm

Radius of Curvature, R = 2f = 2*80cm = +160cm

Hence, R = +160cm

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