Question

a convex mirror of focal length produces a real and inverted image of magnification 0.5. by how much distance the object should be brought closer to obtain the virtual and erect image of magnification 2?

Answer 1

To obtain a virtual and erect image of magnification 2, the object should be brought 1 cm closer to the convex mirror.

Step-by-step explanation:

To obtain a virtual and erect image of magnification 2, the object should be brought closer to the convex mirror. Let's assume the initial distance of the object from the mirror as 'd' and the focal length of the mirror as 'f'. We can use the magnification formula, M = -d/i, where M is the magnification, d is the object distance, and i is the image distance.

Given that the magnification for the real and inverted image is 0.5, we can write the equation as 0.5 = -d/i. Rearranging the equation, we get i = -2d.

To find the new object distance, we need to consider the magnification formula for the virtual and erect image of magnification 2. Substituting M = 2 and i = -2d into the formula, we get 2 = -d/(-2d). Simplifying the equation, we get d = 1 cm.

Therefore, the object should be brought 1 cm closer to the convex mirror to obtain the desired virtual and erect image of magnification 2.