An object is placed 35 cm away from a convex mirror with a focal length of magnitude 15 cm. What is the location of the image?

Let's understand how a convex mirror forms images. In a convex mirror, the center of curvature and the focal point lie behind the mirror. Convex mirrors always produce virtual, upright, and diminished images.
Here, we are given that the object is placed 35 cm away from the convex mirror and the mirror has a focal length of 15 cm.
To find the location of the image, we can use the mirror formula, which states:
1/f = 1/v - 1/u
Where: - f is the focal length of the mirror, - v is the distance of the image from the mirror (negative for virtual image), - u is the distance of the object from the mirror (negative for real object in front of the mirror).
In this case, f = 15 cm and u = -35 cm (negative because the object is in front of the mirror).
Substituting these values into the formula, we get:
1/15 = 1/v - 1/-35
Simplifying the equation, we get:
1/v = 1/15 + 1/35
To add the fractions, we find the common denominator, which is 105. Then, we have:
1/v = (7 + 3)/105
1/v = 10/105
Simplifying further, we get:
1/v = 2/21
To solve for v, we take the reciprocal on both sides of the equation:
v = 21/2
Therefore, the location of the image is 10.5 cm behind the mirror.