calculate the image positions and magnifications for an object 3cm tall and a mirror of focal length +12 with the object at the following positions: 2.5 f, 2.0 f, 1.5 f, 0.5 f.
please help me don't understand it at all.
it would be best if you can explain it to me rather than just giving the answer! thnx
help me pleaseee, i don't get it!!!
sorry, optics is not my thing at all :(
aww okay but thanks anyways
Sure! I'd be happy to explain. To calculate the image positions and magnifications of an object in front of a mirror, we can use the mirror equation and the magnification equation.
The mirror equation is:
1/f = 1/do + 1/di
Where:
- f is the focal length of the mirror
- do is the object distance (distance between the object and the mirror)
- di is the image distance (distance between the image and the mirror)
The magnification equation is:
magnification = di/do
Where:
- magnification represents the size of the image relative to the size of the object. If magnification > 1, the image is larger than the object. If magnification < 1, the image is smaller than the object. If magnification = 1, the image is the same size as the object.
Now, let's calculate the image positions and magnifications for the given object distances.
1. For an object distance of 2.5f:
- Given: do = 2.5f = 2.5 * 12 = 30 cm
- Using the mirror equation: 1/f = 1/do + 1/di
- Rearranging the equation: 1/di = 1/f - 1/do
- Plugging in the values: 1/di = 1/12 - 1/30
- Simplifying: 1/di = (30 - 12)/360
- Calculating: 1/di = 18/360 = 1/20
- Taking the reciprocal: di = 20 cm (image distance)
- Calculating the magnification: magnification = di/do = 20/30 = 2/3
So, for an object distance of 2.5f, the image distance is 20 cm and the magnification is 2/3.
2. For an object distance of 2.0f:
- Repeat the same steps as above, but now with do = 2.0f = 2.0 * 12 = 24 cm
- Calculate the image distance (di) and the magnification.
3. For an object distance of 1.5f:
- Repeat the steps with do = 1.5f = 1.5 * 12 = 18 cm
- Calculate di and the magnification.
4. For an object distance of 0.5f:
- Repeat the steps with do = 0.5f = 0.5 * 12 = 6 cm
- Calculate di and the magnification.
By following the steps mentioned for each object distance value, you'll be able to calculate the image positions and magnifications.