1. Given Data

• Total Magnification (M): 30
• Focal Length of Objective (f_o): 1.25 cm
• Focal Length of Eyepiece (f_e): 5 cm
• Least Distance of Distinct Vision (D): 25 cm

2. Calculating Eyepiece Magnification (m_e)

When the final image is at the near point, the magnification of the eyepiece is:

m_e = 1 + D/f_e

m_e = 1 + 25/5

m_e = 1 + 5 = 6

3. Calculating Objective Magnification (m_o)

The total magnification (M) is the product of the individual magnifications:

M = m_o × m_e

30 = m_o × 6

m_o = 30 / 6 = 5

4. Setup Calculation

Step A: For the Objective Lens

Since m_o = v_o / |u_o| = 5, we have v_o = 5|u_o|.

Using the lens formula (1/v_o - 1/u_o = 1/f_o) and sign conventions (u_o is negative):

1/(5u) - 1/(-u) = 1/1.25

1/5u + 1/u = 1/1.25

(1 + 5) / 5u = 1/1.25

6 / 5u = 1/1.25

5u = 6 × 1.25

5u = 7.5

u = 1.5 cm (Object distance from objective)

Consequently, image distance v_o = 5 × 1.5 = 7.5 cm.

Step B: For the Eyepiece Lens

The final image is at D, so v_e = -25 cm.

Using the lens formula:

1/u_e = 1/v_e - 1/f_e

1/u_e = 1/(-25) - 1/5

1/u_e = (-1 - 5) / 25

1/u_e = -6 / 25

u_e = -25 / 6

|u_e| ≈ 4.17 cm

5. Final Setup Configuration

Separation between lenses (L):

L = |v_o| + |u_e|

L = 7.5 + 4.17

L = 11.67 cm