An object is kept 50cm in front of a convex mirror.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?

Due to the plane mirror, the image is formed 30m opposite to the object inside the mirror. Since theere is no parallax, it means that the images formed due to both the mirrors are at the same position. So for the convex mirror, the value of v is -10. The distance between the object and the mirror is 50. So u = +50. By using the mirror formula, we get

 

1/f = 1/u +1/v

or, 1/f = 1/50 - 1/10 = -4/50

so, f = -50/4

 

So R=2f = 50/2 = 25 cm