Final answer:
The distance required between the objective and the eyepiece to achieve a 10x magnification, with their focal lengths being 3 cm and 10 cm respectively, is 30 cm.
Step-by-step explanation:
To determine the distance between the objective and the eyepiece of a microscope for a required magnification, we can use the formula for magnification in a compound microscope, M = -L/(f_o*f_e), where M is the magnification, L is the tube length (distance between the objective and the eyepiece), f_o is the focal length of the objective lens, and f_e is the focal length of the eyepiece lens.
For this particular problem, we are looking for a 10x magnification with the focal lengths of the objective lens and the eyepiece given as 3 cm and 10 cm respectively.
Rearranging the formula to solve for L, we get L = -M * f_o * f_e. Substituting the given values, we get L = -10 * 3 cm * 10 cm = -300 cm. Because distances in optics are usually taken as absolute values unless we are specifically concerned about the direction of the image formation, we can take the tube length to be 30 cm. Thus, the correct answer is d. 30 cm.