A spherical mirror is polished on both sides. When the concave side is used as a mirror, the magnification is +3.2. 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.
-0.3125
Well, isn't that a reflective situation we have here? When it comes to a spherical mirror, things can get a little twisted. Let me just juggle this information for you, and we'll figure out the magnification on the convex side.
Now, when the concave side is used as a mirror and we get a magnification of +3.2, it means that the image is larger than the object. But now, the convex side steps into the spotlight as the mirror, and we need to determine its magnification.
Since the object remains the same distance from the mirror, let's see... Ah, got it! When the convex side is used, the magnification will be the practical joker amongst numbers, a negative one. That's right, if the object is inverted, the magnification on the convex side will be negative.
So, drumroll, please! The answer to your question is a negative number. Happy mirror pondering!
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 = focal length of the mirror
v = image distance from the mirror
u = object distance from the mirror
Since the object remains the same distance from the mirror, we can use the same values of v and u as before.
Given that the magnification (M) when the concave side is used as a mirror is +3.2, we can use the magnification formula:
M = -v/u
Rearranging the formula, we get:
v = -M * u
Substituting the values:
v = -3.2 * u
Now, we need to find the focal length (f) of the spherical mirror when the concave side is used.
Using the magnification formula for a spherical mirror:
M = -f/u
Substituting the values:
3.2 = -f/u
Rearranging the formula, we get:
f = -u/3.2
Since the mirror is polished on both sides and has the same focal length for both concave and convex sides, the focal length (f) remains the same.
Now, let's find the magnification when the convex side is used.
Using the mirror formula:
1/f = 1/v - 1/u
Substituting the focal length (f):
1/(-u/3.2) = 1/v - 1/u
Rearranging the formula, we get:
1/v = 1/u + 1/u/(-u/3.2)
= 4.2/u
Now, using the magnification formula for the convex side:
M = -v/u
Substituting the values:
M = -(-4.2/u)/u
= 4.2/u^2
Therefore, the magnification when the convex side is used as a mirror, with the object remaining the same distance from the mirror, is +4.2/u^2.
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.
Since the object remains at the same distance from the mirror, the object distance (u) will be the same as before.
Given that the magnification when the concave side is used is +3.2, we can use the magnification formula to find the magnification (m) when the convex side is used:
m = -v/u
Since the object is inverted, the magnification will be negative.
To find the magnification (m) when the convex side is used, we need to find the image distance (v).
We can rearrange the mirror formula to solve for v:
1/v = 1/f + 1/u
Since the mirror is polished on both sides, the focal length (f) will be the same for both sides.
Let's assume the focal length of the mirror is denoted by 'f'. Rearranging the formula, we get:
v = 1 / (1/f + 1/u)
Now, substituting the magnification and object distance, we can find the image distance when the concave side is used as a mirror:
v = 1 / (1/f + 1/u)
v = 1 / (1/f + 1/u)
v = 1 / (1/f - 1/u) (since the magnification is positive)
v = 1 / (1/f - 1/u)
v = u / (u/f - 1)
v = u(f / u) / (f - u) (taking the reciprocal)
v = f / (f - u)
Now, we know that the magnification (m) is given by m = -v/u. Substituting the values, we can find the magnification when the convex side is used:
m = -v/u
m = - (f / (f - u)) / u
m = -f / ((f - u)u)
Please note that the final expression for magnification will depend on the specific values of the focal length (f) and object distance (u) of the spherical mirror being used.