1. Given Data

• Focal length of Objective (f_o): 8.0 mm = 0.8 cm
• Focal length of Eyepiece (f_e): 2.5 cm
• Object Distance (u_o): -9.0 mm = -0.9 cm
• Least Distance of Distinct Vision (D): 25 cm

[Image of compound microscope ray diagram]

2. For Objective Lens

Using the lens formula to find the image distance (v_o):

1/v_o - 1/u_o = 1/f_o

Rearranging:

1/v_o = 1/f_o + 1/u_o

Substituting values (in cm):

• 1/v_o = 1/0.8 + 1/(-0.9)
• 1/v_o = 10/8 - 10/9
• 1/v_o = 1.25 - 1.11
• 1/v_o = 0.1389
• v_o = 1 / 0.1389
• v_o = 7.2 cm

3. For Eyepiece Lens

For the final image to be at the near point, the image distance (v_e) is equal to -D.

• v_e = -25 cm
• f_e = 2.5 cm

Using the lens formula to find object distance (u_e):

1/u_e = 1/v_e - 1/f_e

1/u_e = 1/(-25) - 1/2.5

1/u_e = -1/25 - 10/25

1/u_e = -11/25

u_e = -25/11

|u_e| = 2.27 cm

4. Final Results

(a) Separation between lenses (L)

L = |v_o| + |u_e|

L = 7.2 + 2.27

L = 9.47 cm

(b) Magnifying Power (M)

M = M_o × M_e

M = (v_o / u_o) × (1 + D/f_e)

M = (7.2 / 0.9) × (1 + 25/2.5)

M = 8 × (1 + 10)

M = 8 × 11

M = 88