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.

To find the location and nature of the image formed by a concave lens, we can use the lens equation:

1/f = 1/v - 1/u

Where:
f = focal length of the lens (given as 3 cm)
v = image distance from the lens
u = object distance from the lens (given as -4 cm, negative because the object is placed in front of the lens)

Substituting the given values into the lens equation, we have:

1/3 = 1/v - 1/-4

Since the reciprocal of a negative number is also negative, the equation becomes:

1/3 = 1/v + 1/4

To solve this equation, we need to find a common denominator. Multiplying both sides of the equation by 12 (the least common multiple of 3 and 4), we get:

4 = 12/v + 3

Rearranging the equation, we have:

4 - 3 = 12/v

1 = 12/v

Cross-multiplying, we obtain:

v = 12 cm

Now that we have the image distance, we can determine the nature of the image. If the image distance (v) is positive, it means the image is formed on the opposite side of the lens from the object, i.e., it is a real image. If v is negative, the image is formed on the same side as the object, i.e., it is a virtual image.

In this case, since v = 12 cm, which is positive, the image is a real image formed 12 cm from the concave lens.