An object is placed 4 cm in front of a convex 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 where the image will form and determine whether it is real or virtual, we can use the lens equation:
1/f = 1/v - 1/u
Where:
- f is the focal length of the convex lens
- v is the image distance from the lens (positive if the image is formed on the opposite side of the lens from the object)
- u is the object distance from the lens (positive if the object is on the same side of the lens as the light source)
In this case, the object is placed 4 cm in front of the convex lens (u = -4 cm) and the focal length of the lens is 3 cm (f = 3 cm).
Substituting these values into the lens equation, we get:
1/3 = 1/v - 1/-4
Simplifying further, we have:
1/3 = 1/v + 1/4
To solve for v, we can use algebraic manipulation:
Multiply both sides by 12v to eliminate the denominators:
4v = 12 + 3v
Rearrange the equation to isolate v terms:
4v - 3v = 12
v = 12
So, the image will form 12 cm from the lens.
Now, to determine whether the image is real or virtual, we look at the sign convention:
- If v is positive, the image is formed on the opposite side of the lens from the object, hence it is a real image.
- If v is negative, the image is formed on the same side as the object, hence it is a virtual image.
In our case, v is positive (v = 12 cm), so the image is a real image.