An object is 20cm from a convex lens and produce an image which is three times bigger than the object. What is the focal length of the lens

Answer 1

Let's assume that the object distance is given by u, the image distance is given by v, and the focal length is given by f.

According to the magnification equation:

magnification (m) = -(v/u)

Given that the image is three times bigger than the object, the magnification is 3:

3 = -(v/u)

Solving for "v" in terms of "u":

v = -3u

Using the lens formula:

1/f = (1/v) - (1/u)

Substituting the values of v and u:

1/f = (1/-3u) - (1/u)

Simplifying the equation:

1/f = (-1 - 3)/(-3u)

1/f = (-4)/(-3u)

1/f = 4/(3u)

Rearranging the equation:

f = (3u)/4

Given that the object distance (u) is 20cm:

f = (3 * 20) / 4
f = 60 / 4
f = 15 cm

Therefore, the focal length of the convex lens is 15 cm.