To determine the distance at which the object must have been placed, given that an image is formed at a distance of 24 cm and is 4 times magnified, we can use the magnification formula. Follow these steps:
1. Understand magnification: Magnification (M) is defined as the ratio of the image distance ([tex]\(d_i\)[/tex]) to the object distance ([tex]\(d_o\)[/tex]). The formula is:
[tex]\[
M = \frac{d_i}{d_o}
\][/tex]
2. Given values:
- Image distance ([tex]\(d_i\)[/tex]): 24 cm
- Magnification ([tex]\(M\)[/tex]): 4
3. Rearrange the magnification formula to solve for the object distance ([tex]\(d_o\)[/tex]):
[tex]\[
d_o = \frac{d_i}{M}
\][/tex]
4. Substitute the given values into the formula:
[tex]\[
d_o = \frac{24 \text{ cm}}{4}
\][/tex]
5. Calculate the object distance ([tex]\(d_o\)[/tex]):
[tex]\[
d_o = 6 \text{ cm}
\][/tex]
6. Conclusion: Therefore, the object must have been placed at a distance of 6 cm.
So, the correct answer is:
b. 6 cm
