An object is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position of the image.2.14 cm20 cm5.28 cm8.57 cm

The formula for the image distance (v) in a convex mirror is given by the mirror formula:

1/v = 1/f - 1/u

Where:

• f is the focal length of the mirror
• u is the object distance

For a convex mirror, the focal length (f) is given by f = -R/2, where R is the radius of curvature. In this case, R = 30 cm, so f = -30/2 = -15 cm.

The object distance (u) is -20 cm (it's negative because the object is on the same side of the mirror as the light source).

Substituting these values into the mirror formula gives:

1/v = 1/(-15) - 1/(-20)

Solving this equation for v gives v = -60/7 cm, or approximately -8.57 cm.

The negative sign indicates that the image is formed on the same side as the light source, which is characteristic of virtual images formed by convex mirrors. So, the position of the image is approximately 8.57 cm behind the mirror. Therefore, the correct answer is 8.57 cm.