Question

An objects distance is 2m Infront of the convex mirror and the image height is 1/16 times the object height. What is the focal length of the mirror?

Answer 1

We can use the mirror formula to find the focal length of the convex mirror. The mirror formula is given by:

1/f = 1/v - 1/u,

where f is the focal length, v is the image distance, and u is the object distance.

In this case, the object is located 2m in front of the convex mirror, so u = -2m (negative because the object is in front of the mirror). The image height (h') is 1/16 times the object height (h), so h'/h = 1/16.

We can use the magnification formula, h'/h = v/u, to find the image distance:

1/16 = v/-2.

Simplifying, we find:

v = -2/16 = -1/8.

Now, substituting the values into the mirror formula, we have:

1/f = (1/-1/8) - (1/-2).

Simplifying, we find:

1/f = -8 + 4 = -4.

Taking the reciprocal, we find the focal length of the convex mirror:

f = -1/4 = -0.25m.

Therefore, the focal length of the convex mirror is -0.25m.