A pen placed 13.0 cm from a concave spherical mirror produces a real image 13.5 cm from the mirror.
a) What is the focal length of the mirror? Answer in units of cm.
b) Calculate the magnification of the image.
Assume the pen is placed 28.9 cm from the mirror.
c) What is the position of the new image? (Answer with −1000 if the image does not exist.)Answer in units of cm.
d) What is magnification of the new image? (Answer with −1000 if the image does not exist.)
e) Describe the new image.
1. virtual, inverted, larger
2. real, upright, smaller
3. real, inverted, larger
4. real, upright, larger
5. None of these
6. virtual, upright, smaller
7. real, inverted, smaller
8. virtual, inverted, smaller
9. virtual, upright, larger
To find the answers to these questions, we can use the mirror equation and the magnification equation for concave mirrors.
a) The mirror equation is given by:
1/f = 1/d_o + 1/d_i
Where f is the focal length of the mirror, d_o is the object distance, and d_i is the image distance.
Given that the object distance (d_o) is 13.0 cm and the image distance (d_i) is 13.5 cm, we can substitute these values into the equation and solve for f:
1/f = 1/13.0 + 1/13.5
Solve this equation to find the value of f.
b) The magnification of the image (m) is given by:
m = -d_i/d_o
Substitute the values of d_i and d_o into the equation to calculate the magnification.
c) To find the position of the new image when the object distance (d_o) is 28.9 cm, we can use the mirror equation again:
1/f = 1/d_o + 1/d_i
Substitute the given values and solve for d_i.
If the resulting value of d_i is negative or greater than the distance to the mirror, then the image does not exist, and the answer should be -1000.
d) The magnification of the new image can be calculated using the magnification equation mentioned earlier.
e) To describe the new image, we need to determine whether it is real or virtual, upright or inverted, and larger or smaller. Real images are formed on the opposite side of the mirror from the object and can be projected onto a screen. Virtual images are formed on the same side of the mirror as the object and cannot be projected onto a screen. Upright images have the same orientation as the object, while inverted images have their orientation flipped. Larger images have a larger size than the object, while smaller images have a smaller size.
Based on the calculations of the image position and magnification, we can determine the description of the new image by comparing it to these characteristics.