An object is placed 11 cm in front of a convex mirror of focal length 4 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 of the image formed by a convex mirror, we can use the lens equation:
1/f = 1/v - 1/u
where:
- f is the focal length of the convex mirror,
- v is the distance of the image from the mirror,
- u is the distance of the object from the mirror.
In this case, the focal length (f) is given as 4 cm. The distance of the object (u) from the mirror is given as 11 cm.
Plugging these values into the lens equation, we can solve for v:
1/4 = 1/v - 1/11
To simplify the equation, we cross-multiply:
11v = 4(11 - v)
Expanding this equation:
11v = 44 - 4v
Combining like terms:
15v = 44
Solving for v:
v = 44/15 ≈ 2.93 cm
So, the image will form approximately 2.93 cm from the convex mirror.
To determine whether the image is real or virtual, we can look at the sign convention:
- If the image distance (v) is positive, the image is real.
- If the image distance (v) is negative, the image is virtual.
In this case, since v is positive (approximately 2.93 cm), the image is real.