A spherical mirror is polished on both sides. When the concave side is used as a mirror, the magnification is +3.0. What is the magnification when the convex side is used as a mirror, the object remaining the same distance from the mirror?

0.6

fhg

Well, isn't it fascinating that the mirror gets to have an identity crisis and switch sides? Talk about mirror-fie! Anyway, let's crunch some magnification numbers here.

If the magnification on the concave side is +3.0, it means the image that's formed is three times larger than the object. But now, it's time for the convex side to shine. Pun intended.

Since the object remains the same distance from the mirror, the magnification on the convex side will be slightly different. So, without further ado, drumroll please...

The magnification on the convex side will also be +3.0! That's right, a double whammy of +3.0 magnification! Who knew mirrors could be so consistent?

To find the magnification when the convex side is used as a mirror, 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, and u is the object distance.

Given that the magnification when using the concave side is +3.0, we know that:

magnification = v/u = +3.0

We also know that when the convex side is used as a mirror, the object distance (u) remains the same. Therefore, the image distance (v) will be different.

To find the magnification when using the convex side, we need to determine the focal length of the mirror.

Since the mirror is polished on both sides, it will have the same focal length for the concave and convex side. Hence, the focal length (f) will be the same for both sides.

Now, using the given magnification equation, we can solve for v/u:

v/u = magnification
v/u = +3.0

Next, let's substitute the mirror formula into the magnification equation:

1/f = 1/v - 1/u
1/f = 1/v - 1/u

Since the object distance (u) remains the same, we can ignore it in this case:

1/f = 1/v

Now we can substitute this back into the magnification equation:

v/u = +3.0
1/v = +3.0

Solving for v, we get:

1/v = +3.0
v = 1/3.0
v = 0.33

Now that we have the image distance (v) for the convex side, and the object distance (u) remains the same, we can calculate the magnification for the convex side:

magnification = v/u
magnification = 0.33/u

So, the magnification when the convex side is used as a mirror, with the object remaining at the same distance, is 0.33/u.

To find the magnification when the convex side is used as a mirror, we can make use of the mirror formula:

1/f = 1/v - 1/u

where:
f is the focal length of the mirror,
v is the image distance,
and u is the object distance.

For a spherical mirror, the focal length for the convex side is positive (+) and for the concave side is negative (-).

Given that the magnification when the concave side is used as a mirror is +3.0, we know that:

magnification (m) = -v/u = -3.0

Now, let's consider the case when the convex side is used as a mirror. The object remains the same distance from the mirror, which means the object distance (u) remains unchanged.

To find the magnification (m) when the convex side is used, we need to find the image distance (v) using the mirror formula and then calculate the magnification:

1/f = 1/v - 1/u

Since the object distance (u) remains the same, we can rewrite the mirror formula as:

1/f = 1/v' - 1/u

where v' is the image distance when the convex side is used as a mirror.

Since the magnification is defined as:

m = -v'/u

we can rearrange the equation to solve for v':

v' = -mu

Substituting the given magnification value:

v' = -(-3.0 * u)

Simplifying:

v' = 3.0u

Now we have the image distance (v') when the convex side is used as a mirror. To find the magnification (m), we substitute the values into the magnification formula:

m = -v'/u
= -(3.0u)/u
= -3.0

Therefore, the magnification when the convex side is used as a mirror, with the object remaining the same distance from the mirror, is -3.0.