An angular magnification (magnifying power) of 30X is desired using an objective of focal length 1.25 cm and an eyepiece of focal length 5 cm. How will you set up the compound microscope?
The compound microscope should be set up as follows:
Object distance from objective: 1.5 cm Tube length (L): 6.25 cm Separation between objective and eyepiece: 11.67 cm
This configuration produces an angular magnification of 30X with the final image formed at the near point (25 cm).
Explanation
This question tests understanding of compound microscope configuration. The textbook provides the formula for total magnification when the final image is at the near point: m = (L/f_o) × (1 + D/f_e), where L is the tube length (distance between focal points of objective and eyepiece), f_o and f_e are focal lengths, and D = 25 cm is the least distance of distinct vision. The setup requires calculating three parameters: tube length, object distance from objective, and lens separation. The object must be placed just beyond the focal point of the objective to form a real, magnified image that serves as the object for the eyepiece.
Solution Steps
Step 1: Calculate tube length (L) using magnification formula for final image at near point: m = (L/f_o) × (1 + D/f_e)
Substituting values: 30 = (L/1.25) × (1 + 25/5) = (L/1.25) × 6
Solving: L = / 6 = 6.25 cm
Step 2: Calculate object distance from objective (u_o)
Magnification by objective: m_o = L/f_o = 6.25/1.25 = 5
Using lens formula and m_o = v_o/|u_o| = 5, we get: |u_o| = 6f_o/5 = /5 = 1.5 cm
Step 3: Calculate separation between lenses
Image distance from objective: v_o = = 7.5 cm
For eyepiece with image at near point: 1/v_e - 1/u_e = 1/f_e, where v_e = -25 cm
Solving: u_e = -25/6 -4.17 cm
Separation: d = v_o + |u_e| = 7.5 + 4.17 11.67 cm