An object is placed 4 cm in front of a concave lens of focal length 3 cm. Using the lens equation, find where the image will form and state whether it is a real or virtual image.
12cm real image
To find where the image will form and determine whether it is real or virtual, we can use the lens equation, which is:
1/f = 1/v - 1/u
where:
f = focal length of the lens (given as 3 cm)
v = image distance
u = object distance (given as 4 cm)
Substituting the given values into the equation, we have:
1/3 = 1/v - 1/4
To solve for v, let's simplify the equation:
1/v = 1/3 + 1/4
1/v = (4 + 3) / (3 * 4)
1/v = 7/12
To isolate v, we take the reciprocal of both sides of the equation:
v = 12/7
Therefore, the image will form at a distance of 12/7 cm from the lens.
To determine if the image is real or virtual, we look at the sign convention used for distances. In this case, the object distance (u) is positive since the object is placed in front of the lens, and the lens is concave. Using the lens equation, we find that the image distance (v) is also positive.
A positive image distance corresponds to a real image. So, in this case, the image formed is real.