A spherical mirror is polished on both sides. When the concave side is used as a mirror, the magnification is +2.7. What is the magnification when the convex side is used as a mirror, the object remaining the same distance from the mirror? If the object is inverted, then enter a negative number. Otherwise, enter a positive number.
To find the magnification when the convex side of the spherical mirror is used, we can use the mirror formula:
1/f = 1/v - 1/u
where
- f is the focal length of the mirror,
- v is the image distance from the mirror, and
- u is the object distance from the mirror.
Since the object distance remains the same, we can use the magnification formula:
magnification = -v/u
Given that the magnification on the concave side is +2.7, we can use this information to find the focal length of the mirror. For a concave mirror, the magnification is positive and the focal length is positive.
Using the given magnification (magnification = +2.7), we first calculate the focal length:
magnification = +2.7 = -v/u
v = -2.7u
Substituting this value of v into the mirror formula:
1/f = 1/v - 1/u
1/f = 1/(-2.7u) - 1/u
1/f = -0.3704/u
To solve for f, we need to know the object distance u.
Once we have the focal length of the concave side, we can find the magnification on the convex side using the same formula:
magnification = -v/u
Given that the object remains the same distance from the mirror:
u (concave) = u (convex)
Substituting the focal length (f) calculated earlier into the mirror formula:
1/f = 1/v - 1/u
Solve for v
Then substitute the values of f and v into the magnification formula:
magnification (convex) = -v/u
This will give us the magnification on the convex side of the spherical mirror.