A convex spherical mirror of focal length 15.0 cm is to form an image 9.00 cm from the mirror. Where will the object be placed?
A man standing 1.25 m in front of a shaving mirror produces an inverted image 25.0 cm in front of it. How close to the mirror should he stand if he wants to form an upright image of his chin that is twice the actual size of his chin?
You have two completely different questions here. I will answer the second of them.
Use the information on where the inverted (real) image forms to get the focal length of the mirror.
1/125 + 1/25 = 1/f = 6/125
f = 125/6 = 20.83 cm
For the upright image with a magnification of 2, use the same focal length but use di/do = -2 to solve for do
1/do + 1/di = 1/do - 1/(2 do) = 1/20.83
1/(2 do) = 1/20.83
do = 10.42 cm
To find the position of the object in front of the convex spherical mirror, we can use the mirror equation, which relates the object distance (denoted by "u"), the image distance (denoted by "v"), and the focal length (denoted by "f") of the mirror:
1/f = 1/v - 1/u
Given that the focal length (f) is 15.0 cm and the image distance (v) is 9.00 cm, we can rearrange the equation to solve for the object distance (u).
1/f + 1/u = 1/v
Substituting the given values:
1/15 + 1/u = 1/9
Let's solve this equation:
Multiply through by 135u to eliminate the fractions:
9u + 15u = 15 * 135
24u = 2025
Dividing both sides by 24:
u = 2025 / 24
Simplifying further:
u ≈ 84.375
Therefore, the object must be placed approximately 84.375 cm in front of the convex spherical mirror.